Final Exam Comprehensive Review

Solving Two-Step Equations Lesson

By: J. Deberry

Integers Review!

• Examples:

  • 5 + (-12) =

  • 9 - (-3) =

  • -4 x (-2) =

  • -12 / 4 =​

Multiple Choice

Quick Check:

When you add numbers with DIFFERENT signs you....

• Subtract, then take the sign of the BIGGER number

• Add, then take the sign of the SMALLER number

• Add normally

• Do nothing

Multiple Select

Quick Check:

Same signs = POSITIVE answer

This is the rule for...

• Adding integers

• Subtracting integers

• Multiplying integers

• Dividing integers

Multiple Choice

Quick Check:

Choose the EQUIVALENT expression for 14 - 25

• 14 + 25

• 14 - (-25)

• 14 + (-25)

​Solving Equations Check-list

• ​The OPPOSITE of the Order of Operations

• Ask yourself... "Do I see [operation]? If so, do the OPPOSITE!

• You aren't finished unless you have a checkmark for all four operations!​

Multiple Choice

Quick Check:

What comes first when solving the equation 5x + 3 = -7?

• Divide by 5

• Add 3

• Subtract 3

• Multiply by 5

Fill in the Blank

Solve: 5x + 3 = -7

Multiple Choice

Quick Check:

What comes first when solving the equation x/6 - 4 = -10?

• Add 4

• Subtract 4

• Divide by 6

• Multiply by 6

Fill in the Blank

Solve: x/6 - 4 = -10

How do I know if I'm correct?!

• Remember substituting variables?

• Whatever solution you find, plug it back into your equation.

• If the sentence is TRUE, your answer is correct!​

• Example: Who is correct?

  • Sally says the solution to 6x + 3 = 27 is x=7

  • Sam says the solution to 6x + 3 = 27 is x=4​

Multiple Choice

Quick Check:

-3x - 5 = -11

Solution: x = 2

True or False?

• True

• False

Multiple Choice

What does isolate the variable mean?

• Get the variable alone

• Get rid of the variable

Our Strategy

• Keep it balanced

• What you do to one side, do to the other

• "Copy and Paste"

Use Inverse Operations to isolate the variable

• Inverse of addition - subtraction

• Inverse of subtraction - addition

• Inverse of multiplication - division

• Inverse of division - multiplication

Multiple Choice

What is the inverse of multiplication?

• Addition

• Subtraction

• Multiplication

• Division

3x - 6 = 12

• Add 6 to both sides: 3x = 18

• Divide both sides by 3: x = 6

• Check: 3(6) - 6 = 18 - 6 = 12

Check:  4(2.5) + 5 = 10 + 5 = 15

Multiple Choice

12g - 5 = 19

Which is the correct 1st step?

• Add 12 to both sides

• Add 5 to both sides

• Add 19 to both sides

Multiple Choice

$$12g-5=19$$  

$$\ \ \ \ \ \ \ +5\ \ \ \ +5\ \ \ \ \ \ \ \$$  
$$12g\ \ \ \ \ \ \ =\ 24$$  
What is the next step?

• Multiply both sides by 12

• Divide both sides by 12

• Multiply both sides by 24

• Divide both sides by 24

Multiple Choice

2t -7 = 3

Find the value of t

• -2

• 2

• 5

• 20

Multiple Choice

$$\frac{2}{5}\ h\ +\ 6\ =\ 8$$  


What is the first step that should be done to both sides?

• +6

• -6

• +8

• -8

Multiple Choice

$$\frac{2}{5}\ h\ =\ 2$$  


What is the second step that should be done to both sides? 

• $$+\ \frac{5}{2}$$  

• $$-\ \frac{5}{2}$$  

• $$\cdot\ \frac{5}{2}\$$  

• $$\div\ \frac{5}{2}$$  

Multiple Choice

$$\frac{2}{5}\ h\ =\ 2$$  

What is the value of h?

• $$\frac{4}{5}$$  

• $$2\ \frac{2}{5}$$  

• 2

• 5

Multiple Choice

10 = 2d - 5

What is the value of d?

• 2.5

• 7.5

• 15

• 20

Multiple Choice

$$\frac{2}{3}x\ +\ 1\ =\ \frac{5}{3}$$  

What is the value of x?

• 0

• 1

• 2

• 3

The Distributive Property

Fill in the Blank

Solve the equation

12x - 15 = 3(2x+3)

Multiple Choice

Solve:
5y+34 = -2(-7y+1)

• y = -4
• y = 9
• y = 4
• y = 36/19

Solution Types

Multiple Choice

$$7x-3=7x+5$$  

• No Solution

• Infinite Solutions

• $$x=2$$  

• $$x=8$$  

Multiple Choice

5x + 6 = 2 + 3x

• one solution x = -2

• no solutions

• infinite solutions

• one solution x = 2

Multiple Choice

$$6x+5=8+4x+2x$$  

• No Solution

• Infinite Solutions

• $$x=3$$  

• $$x=13$$  

Multiple Choice

3x + 15 = 3(x + 5)

• No Solution
• x = 15
• Infinitely Many Solutions

Multiple Choice

6x - 8x + 5 = -2(x + 2) + 7

• One solution

• No solution

• Infinitely Many

Distributive Property

a(b+c)= ab + ac

​

or

​

a(b-c) = ab-ac​

​

​

Subject | Subject

Some text here about the topic of discussion

Inequalities

What is an inequality?

How are equations and inequalities different?

Equations

Have an = sign

Only have one answer when solved

Inequalities

Don't have and = sign instead use inequality symbols

< (less than)

> (greater than)

≤ (less than or equal to)

≥ (greater than or equal to)

Can have multiple answers when solved

Example of an inequality and how to interpret your answer.

Multiple Choice

Solve the following inequality:

x + 2 > 12

• subtract 2 from both sides and your answer is

  x = 10

• subtract 2 from both sides and your answer is

  x > 10

• subtract 2 from both sides and your answer is

  X < 10

Multiple Choice

Solve 5x > 10

• divide by 5 on both sides and your answer is

  x = 2

• divide by 5 on both sides and your answer is

  x < 2

• divide by 5 on both sides and your answer is

  x > 2

Multiple Choice

Solve 3x + 2 > 8

• subtract 2 from both sides and your answer is

  x > 6

• subtract 2 from both sides and your answer is

  x = 6

• subtract 2 from both sides and then divide by 3 on both sides and your answer is

  x > 2

Multiple Choice

Solve the inequality

3x - 7 < 5

• x < 4

• x < -2

• x = 4

One Rule: If you are multiplying or dividing by a negative number you must switch the direction of the inequality symbol. 

• (ex) Solve -4x > -12

• Divide both sides by -4, and because we are dividing by a negative number, we must reverse the inequality sign

  ⇒ -4x/-4 < -12/-4

  ⇒ x < 3

Multiple Choice

Try some:

-2x ≤ 4

• divide by -2 o both sided and your answer will be

  x = -2

• divide by -2 on both sides and you will switch the direction of the inequality since you are dividing by a negative and your answer will be

  x ≥ -2

• divide by -2 on both sides and your answer will be

  x ≤ -2

Multiple Choice

- 3x < -12

• divide both sides by -3 and your answer is

  x < 4

• x = 4

• divide both sides by -3 and your answer is

  x > 4

  because you divided by a negative and had to flip the inequality symbol

Multiple Choice

Example

$$\frac{x}{-2}\ge3$$

• multiply both sides by -2 and your answer will be

  x ≤ -6

  because you multiplied by a negative you must switch the inequality

• multiply both sides by -2 and your answer will be

  x ≥ -6

• divide both sides by -2 and you get

  x ≥ -2/3

GREATER THAN

• is greater than

• is more than

LESS THAN

• is less than

• is fewer than

GREATER THAN OR EQUAL TO

• is greater than or equal to

• is at least

• is no less than

LESS THAN OR EQUAL TO

• is less than or equal to

• is at most

• is no more than

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

There are fewer than 50 people allowed in this area.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

I need at least 30 orders to meet my qouta.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

I see more than a dozen seagulls.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

WHICH SIGN GOES WITH THE PHRASE?

I can spend no more than $20 at the store.

• $$<$$

• $$>$$

• $$\le$$

• $$\ge$$

Multiple Choice

Each gumball in a gumball machine costs $0.25. You can spend no more than $2.50 in total on gumballs.

Which inequality would represent how many gumballs you could buy?

• $$0.25x\ <\ 2.50$$

• $$0.25x\ >\ 2.50$$

• $$0.25x\ \le\ 2.50$$

• $$0.25x\ \ge\ 2.50$$

Multiple Choice

You have $30 to buy baseball cards. Each pack of cards costs $5. Write an inequality that represents the number of packs of baseball cards you can buy and still have at least $10 left.

• $$30\ -\ 5x\ \ge10$$

• $$30\ -\ 5x\ \le\ 10$$

• $$30\ -\ 5x\ <\ 10$$

• $$30\ -\ 5x\ >\ 10$$

GRAPH OF AN INEQUALITY

Multiple Choice

WHICH INEQUALITY IS REPRESENTED BY THE GRAPH?

• $$X\ <\ 1$$

• $$X\ \le\ 1$$

• $$X\ >\ 1$$

• $$X\ \ge\ 1$$

Multiple Choice

WHICH INEQUALITY IS REPRESENTED BY THE GRAPH?

• $$X\ <\ 2$$  

• $$X\ \ge\ 2$$  

• $$X\ >\ 2$$  

• $$X\ \le\ 2$$  

Compound Inequalities

AND vs OR

• Compound Inequalities have two inequalities attached to each other and mean that both statements are true.

• When you graph an AND inequality, the arrows will point to each other.

• When you get an OR inequalities, the arrows will point away from each other

AND

Here is a video on how to solve a Compound Inequality that uses the word AND.

Multiple Choice

Which graph represents the answer to the compound inequality: 

$$4\le x+2\le8$$  ?

Correct Answer

Multiple Choice

Which graph represents the answer to the compound inequality: 

$$-9<x-10<5$$  ?

Correct Answer

Multiple Choice

Which graph represents the answer to the compound inequality: 

$$-50<7x+6<-8$$  ?

Correct Answer

This one requires two steps.

Unit Rates

By Susan Kahler

​Remember that when you divide fractions, the rule is multiply by the reciprocal. (Keep, Change, Flip)

​It is ok to get a decimal or a fraction when you do this. Look at the examples below

You will have some unit rates where you are asked to work with mixed numbers as shown on the left.

When given mixed numbers turn them into improper fractions before dividing.

Remember when you divide fractions follow the Keep Change Flip pattern. ​

Example with Complex Fractions

Some text here about the topic of discussion

Fill in the Blank

Johnny read 300 words in 6 minutes. At what rate, words per minute, is Jonny reading? ( Since you want words per minute, words goes on top and minutes goes on the bottom)

Fill in the Blank

A teacher sharpens 108 pencils to distribute to her 27 kindergarten students. How many pencils should each student get? Express as pencils per student. ( $$\frac{pencils}{students}$$  )

Fill in the Blank

George finished 1/4 of a level of his computer game in 1/3 of an hour. How many hours will it take him to complete one level?

Multiple Choice

Betty makes pies. To make 6 pies, she uses $$7\ \frac{1}{2}$$  Cups of flour. How many cups of flour are needed to make 1 pie? ( Because you want 1 pie your fraction is $$\frac{flour\ }{pie}$$  )

• $$1\ \frac{1}{4}$$  cups

• 45 cups

• 1/45 cups

• 1/4 cup

Multiple Choice

• Sue's

• Millie's

• Tamira's

• Creative

Multiple Choice

• Marcus

• Joseph

• Harper

• Nikki

Multiple Choice

Six tubs of frosting costs $5. How much is it for 1 tub of frosting?

• $1 per tub

• $8.30 per tub

• $0.83 per tub

• $0.08 per tub

Multiple Choice

A piano teacher charges $200 for 12 piano lessons. How much is it for one piano lesson?

• $16.67 per lesson

• $17 per lesson

• $1.67 per lesson

• $16 per lesson

Multiple Choice

A company charges $2.95 for 24 bottles of water. What is the cost per bottle of water?

• $0.12 per bottle

• $8.14 per bottle

• $0.25 per bottle

• $1.12 per bottle

Multiple Choice

Jane is buying coffee. Coffee Shop A sells 30 ounces for $9.95 and Coffee Shop B sells 12 ounces for $3.50. Which coffee shop is cheaper per ounce?

• A because they are selling you more coffee in total

• A because there unit price is $0.29 per ounce where B is $0.33 per ounce

• B because their unit price is $0.29 per ounce and A is $0.33 per ounce

Unit 3 - Ratios & Proportional Relationships Review

Fill in the Blank

Solve using the distributive property

7(x+4)

An equation stating that two ratios are EQUAL.

Is a fraction that compares two different things. The top and the bottom numbers represent different things.

Ratios & Proportions

Ratio​

​Proportion

Fill in the Blank

Solve using the distributive property

-5(m-2)

How do you determine if two ratios are proportional?

Cross-multiply, if the cross-products are the same, the ratios are proportional. If the cross-products are different, the ratios are not proportional

Fill in the Blank

Solve using the distributive property

-4 (-w-10)

Multiple Choice

Which two ratios form a proportion?

• $$\frac{8}{12}\ and\ \frac{4}{8}$$  

• $$\frac{8}{12}\ and\ \frac{1}{4}$$  

• $$\frac{8}{12}\ and\ \frac{4}{6}$$  

• $$\frac{8}{12}and\ \frac{4}{1}$$  

Fill in the Blank

Solve using the distributive property

6a(b + 2c)

Multiple Choice

Suzanne can work 10 math problems in 15 minutes. How many can she work in an hour and a half?

• 45

• 60

• 70

• 75

Fill in the Blank

Solve using the distributive property

2(x- y + 8)

How to identify proportional relationships in EQUATIONS

​Must be in the form y = kx

- NO adding or subtracting

​- if it is division, variable must be on the top, NOT THE BOTTOM

Fill in the Blank

Solve using the distributive property

x(2y -5z + 1)

Multiple Choice

Which equation represents a proportional relationship?

• $$y=\frac{1}{2}x$$  

• $$y=\frac{1}{2}x+1$$  

• $$y=\frac{1}{2}x+2$$  

• $$y=\frac{1}{2}x+\frac{1}{2}$$  

Fill in the Blank

Solve using the distributive property

$$\frac{1}{4}\left(8x-4\right)$$  

How to identify proportional relationships in TABLES

​Cross-products or quotients must be the same!!

Look at the examples:

Fill in the Blank

Solve using the distributive property

$$\frac{1}{6}\left(\frac{3}{5}x+18\right)$$  

Multiple Choice

Is this table proportional or non-proportional?

• Proportional
• Non-Proportional
• both
• neither

Distributing and Combine!

To simplify an expression means to ensure there are no parentheses and no like terms. In order to do this, distribute first (if needed), then combine like terms

​

Subject | Subject

Some text here about the topic of discussion

How to identify proportional relationships in GRAPHS

Graphs must do BOTH of these two things:

1. Be a straight line

2. Go through the origin (0,0)​

Steps

Solve

Example

Some text here about the topic of discussion

​1. Distribute

2. Combine Like Terms (16x and -6x)​

3. Done​

​

Multiple Choice

Which graph is proportional?

• A
• B
• C and D
• All of the graphs are proportional

Fill in the Blank

Solve

$$10-\left(y-6\right)-y$$  

Multiple Choice

Is the graph proportional or non proportional?

• proportional
• non proportional

Fill in the Blank

Solve

$$\frac{9}{4}\left(\frac{10}{3}x-4\right)-\frac{1}{4}\left(2x-8\right)$$  

Constant of Proportionality

is the value that is consistently multiplied by the independent variable (x) of a situation

Can also be understood as the unit rate of a situation (the amount per 1 unit)

​Constant of proportionality = k

Divide any non-zero y-value by its corresponding x-value

Tables

k. The number that gets multiplied by x.

y =kx

Example: y = 5x

k = 5 ​

​

Equations

How to find (k) constant of proportionality

Graphs

Find a coordinate pair (x , y) on the line and divide the y by the x​

​Remember that k = y/x

Multiple Choice

In the equation y = 14x, what is the constant of proportionality?

• y
• x
• 14

Examples:

​Remember that k = y/x

​1. What is the constant of proportionality in this table?

2. What is the constant of proportionality in this graph?

​- choose any y-value and its corresponding x-value y=80 x=5

​

- divide y/x 80/5 k=16​

​

​- choose any coordinate pair (point on the graph (x,y) (2,20)

- divide y/x 20/2 k=10​

Multiple Choice

What is the constant of proportionality for this table?

• 1/9
• 9
• 8

Multiple Choice

What is the constant of proportionality for the line on the graph below?

• 2

• 1

• -1

• $$\frac{1}{2}$$

Multiple Select

Check all the words that mean the same thing...

• constant of proportionality

• k

• unit rate

• direct variation

Writing Equations for Proportional Relationships

1.Find k. Remember:

​

Plug in k into the equation y = kx ​

Some text here about the topic of discussion

Multiple Choice

Write an equation for this relationship.

• y=1/5x
• y=1/2x
• y=2x
• y=5x

Multiple Choice

Which equation matches the graph?

• y = 8x
• y = 1x
• y = 3x
• y = 16x

Unit Rate

Is just another word for constant of proportionality

We use rates to COMPARE ratios by dividing by the unit we want to know one of

- Unit rate tells us the rate PER ONE UNIT​

- In unit rates, the denominator is always 1!!!​

Some text here about the topic of discussion

Multiple Choice

Which of these describes the unit rate?

• a unit of measure
• a fraction with a numerator of one
• a fraction with a denominator of one
• a proportion

Multiple Choice

Albert wants to buy some pens. He compares 4 different packs of pens. Which two packs of pens have the same cost per pen?

• Packs 1 and 2

• Packs 1 and 3

• Packs 2 and 4

• Packs 1 and 4

Multiple Choice

Elijah earn $200 for 8 hours of work. What is the unit rate (in dollars per hour)?

• $50 per hour
• $12 per hour
• $192 per hour
• $25 per hour

Multiple Choice

Walmart sells 24 bottles of water for $3 and 36 bottles of water for $4. Which is the better buy and by how much?

• 24 bottles of water for $3 by 1.5 cents per bottle

• 24 bottles for $3 by 0.70 cents per bottle

• 24 bottles for $3 by 0.75 cents per bottle

• 36 bottles for $4 by 1.4 cents per bottle

Multiple Select

A store had 2 blue chairs for $22.78 or 6 red chairs for $67.80. Which color chair has the lower unit price?

• 2 blue chairs for $22.78

• 6 red chairs for $67.80

Multiple Choice

A candy store can make one piece of candy in 15 seconds. What is the rate per minute?

• 2 candies per minute

• 3 candies per minute

• 4 candies per minute

• 5 candies per minute

Unit Rates with Complex Fractions

When you divide a fraction by a fraction that is called a complex fractions

Some text here about the topic of discussion

Multiple Choice

Simplify the complex fraction shown.

• 9/40
• 40/9
• 10/36
• 5/18

Multiple Choice

It took Julius 1/3 of an hour to ride his bike 2 & 3/4 of a mile. How many miles per hour can he ride his bike?

• 3 & 1/2
• 6 & 3/4
• 8 & 1/4
• 16 & 1/2

Multiple Choice

Mr. Roman drove from his hometown to another city. He used 12 & 1/4 gallons of gas for the 318 & 1/2 mile trip. On average, how many miles did Mr. Roman travel per gallon of gas?

• 26
• 26 & 1/2
• 30 & 5/8
• 38 & 4/25

Interpreting Graphs

What does the point (1 , 4) represent?

​Remember:

- a point is written as (x, y)

​- the x-values are on the horizontal axis

​

​

​Answer: In 1 hour, they travel 4 miles.

Multiple Choice

Choose the best explaination

• Taylor can write 6 words per minute
• Taylor can write 25 words per minute
• Taylor can write 50 words per minute
• Taylor can write 150 words per minute

Multiple Choice

What is the unit rate for the rain fall?

• 2 cm per hour
• 1 cm per hour
• ¹/₂ cm per hour
• 4 cm per hour

Finding Percent

Multiple Choice

60% of the animals at a pet shop are dogs. If there are 42 dogs at the shop, then how many animals are there at the shop?

• 70 animals

• 18 animals

• 60 animals

• 42 animals

Multiple Choice

In a neighborhood, there are 9 families that own a poodle. If these owners make up 50% of all dog owners in the neighborhood, how many dog owners are there?

What part of the percent proportion are you missing?

• Part

• Whole

• Percent

​

​

- What did they pay after discount is applied?

- What is the sale price of the item?​

​

Some will ask you to find the final price after the discount.

Some problems will ask you to find discount amount only.

Discounts & Markdowns

​- How much of a discount did they receive?

- How much did they save?​

​You have to pay attention to what the question is asking!!!

Multiple Choice

A bottle of soda is on sale for 15% off. The soda is $3.50. How much is the bottle of soda after the discount?

• $4.03

• $2.97

• $0.53

• $0.75

Multiple Choice

A clothing store is having a sale for 35% off all clothes. A shirt original price is $69.99. What is the sale price of the shirt?

• $45.49

• $24.50

• $94.49

• $32.59

​

​

Some you have to find the total cost (add the % amount to the original price):

Some you have to find % only:

Tax, Tip, Mark-up, Commission

​Again, you have to pay attention to what the question is asking!!!

​- How much did they pay in sales tax or tip?

- What is the markup amount?

- How much did they pay in commission?​

​- What was the total cost?

- How much did they have to pay back total with the commission?

- What is the profit?​

Multiple Choice

Martin went shopping at a bookstore. The price of the book he selected was $25.99 and the sales tax rate at the bookstore was 4%. What was the sale price of the book?

• $10.40

• $1.04

• $27.03

• $29.99

Multiple Choice

The original price of a collectible train set is $345.75. The sales tax for this train set is 5.5%. What is the sale price of the train set?

• $19.02

• $326.73

• $364.77

• $22.93

Simple Interest

​Use the formula:

Multiple Choice

Maria borrowed $3,000 at a simple interest rate of 4% per year.  How much did she have to repay after 4 years?

• $480
• $3,480
• $4,800
• $7,800

Scale Factors and Scale drawings

Calculating Slope

Slope and Rate of Change

(slope = rate of change)

Slope

The ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).

Four Types of Slope

• Positive: up and to the right OR down and to the left

• Negative: up and to the left OR down and do the right

• Zero: no vertical change, horizontal line 

• Undefined: no horizontal change, vertical line

Multiple Choice

What is the slope of this line?

• Zero

• -2

• undefined

• 8

Slope is represented with the variable, m. 

The change in the y-coordinates is the rise.

The change in the x-coordinates is the run. 

The coordinates that are used when finding slope are labeled as      (x1, y1) and (x2, y2)

Multiple Choice

Identify the type of slope.

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

$$\Delta PQR\ is\ similar\ to\ \Delta STU$$  What side corresponds to side UT?

• PQ

• RQ

• QR

• QP

Multiple Choice

Identify the type of slope.

• Postive

• Negative

• Zero

• Undefined

Multiple Choice

What is the equation for finding slope?

• $$m\ =\ \frac{y2\ -\ y1}{x2\ -\ x1}$$

• $$m\ =\ \frac{y2\ +\ y1}{x2\ +\ x1}$$

• $$m\ =\ \frac{x2\ -\ x1}{y2\ -\ y1}$$

• $$m\ =\ \frac{x2\ +\ x1}{y2\ +\ y1}$$

Multiple Choice

Scale Factor is a ratio comparing:

• the new value to the original value

• the original value to the new value

Slope on a Graph

Finding Slope from a Graph

First, find the rise (the change in the y values)
Second, find the run (the change in the x values)

Multiple Choice

The fraction 1/5 as a constant rate of change will...

• Rise 4, & Run 1

• Rise 5, & Run 5

• Rise 1 , & Run 5

• Rise 5 & Run 1

Multiple Choice

What is the rate of change for the following graph?

• 80

• 20

• 40

• 160

Rise = 6 - 3 = 3
Run = 8 - 4 = 4
Slope = 3/4

Slope from a Table

Multiple Choice

What is the slope shown on the table?

• m = -4

• m = $$\frac{2}{3}$$

• m = $$\frac{3}{2}$$

• m = $$-\frac{2}{3}$$

You can also find slope by counting spaces on the graphs. Remember, slope is rise over run.
How many spaces does the graph go up?
How many spaces does the graph go over?

Slope from Two Ordered Pairs

Multiple Choice

Analyze the point (3, 27). What does the point represent?

• The point (3,27) represents 27 shirts for $3.

• The point (3,27) represents $27 for 3 shirts.

The direction of the line makes a difference whether the slope is positive or negative. 
The red line shows a positive slope.
The blue line shows a negative slope.

Multiple Choice

Find the slope of the line that contains (3, -4) and (-1, 6)

• $$m\ =\ 1$$

• $$m=\frac{5}{2}$$

• $$m=-\frac{5}{2}$$

• $$m=-1$$

Multiple Choice

Triangle PQR is shown. Its original lengths are multiplied by 2.5. What are the new side lengths of P’Q’R’?

• PQ: 20, RQ: 42.5, RP: 37.5

• PQ: 16, RQ: 34, RP: 30

• PQ:4, RQ:8.5, RP: 7.5

Multiple Choice

Find the rate of change between the points (-2 , 10) & (4 , 14)

• 2/3

• -2/3

• 3/2

• 2/1

Multiple Choice

Find the slope.

• 1/2

• 2

• -1/2

• -2

Multiple Choice

Which of the following are ways to find the rate of change?

• change in y over change in x

• rise over run

• subtract y coordinates over subtract x coordinates

• all of the above

Multiple Choice

Rectangle ABCD has been enlarged to form rectangle A’B’C’D’. What is the scale factor?

• 2

• 2.5

• 3

• 3.5

Multiple Choice

Find the slope.

• 1/2

• 2

• -1/2

• -2

Reminder: You have independent practice

1. Classifying Triangles

2. Intro to Scale Factors

Multiple Choice

Find the slope.

• 1

• -1

• 2

• -2

Open Ended

Exit Ticket: Triangle PRQ was enlarged to form triangle SUT. What is the scale factor?

Multiple Choice

Find the slope.

• 1

• -1

• 2

• -2

Slope Recap

Slope = m = rise over run
Direction of line determines whether slope is posititve or negative
Slope is NOT always a whole number. Slope CAN be a fraction!