Math Fundamentals Review #2

Math Fundamentals Review

In order to prepare for the NEXT unit, we are going to review:

• Plugging in BOTH x- and y-values

• Finding the slope of a line using the slope formula

• Finding the slope using RISE/RUN

• Graphing Coordinate Points

Plugging in x- and
y-values

y= 3x + 2

• y= 3(1) + 2

• y= 5

• y= 3(2) + 2

• y= 8

Solving one-step equations

• Use an inverse operation to get to the variable by itself

• Check your answer

Multiple Select

Check all that apply:

2.5 + A = 23.4

• the inverse operation of addition is subtraction

• + 2.5 on both sides

• -2.5 on both sides

• A = 21.1

• Check your answer by replacing the variable with its value

Solve two-step equations

• What are you solving for?

• + or - to isolate the variable term.

• × or ÷ to solve for the variable.

Multiple Select

Check all that apply:

5v + 4 = -26

• First step: +26 on both sides

• First step: -4 on both sides

• Second step: +26 on both sides

• Second step: -5 on both sides

• Second step: divide by 5 on both sides

Fill in the Blank

What is the value of v?

5v + 4 = -26

v = ?

Type the number, no space.

-

Variables on both sides

Move all variable terms to one side

Multiple Choice

How to move all variables to one side?

2x - 4 = x + 5

• +4 on both sides

• -5 on both sides

• +2x on both sides

• -x on both sides

Multiple Select

How to move all variables to one side?

3a + 2 = 8a + 9

• -2 on both sides

• -9 on both sides

• -8a on both sides

• +8a on both sides

• -3a on both sides

Function Notation

• f(x) = 2x + 3, Find f(2)

• f(2) means you are replacing any x's with the number 2 and then evaluating

• 2(2)+3 f(2) = 7

• Always put parenthesis around the number you are subbing

Multiple Choice

g(x) = 3x + 1
g(2) = _______

• 6
• 7
• 8
• 9

Multiple Choice

Solve
4 = 2 + x

• x = 6
• x = 2
• x = 8
• x =-2

Multiple Choice

Solve
12 = y + 5

• y = 17
• y = -7
• y = 8
• y = 7

Multiple Choice

Solve

$$x-5=-8$$  

• x= -3

• x=13

• x= -13

• x= 3

Math Response

Given h(x) = 5 - 9x, find h(8). 

Type answer here

Correct Answer: -67

Deg^°

Rad

Multiple Choice

Evaluate f(-5) if f(x) = -2x - 12

• -22
• -2
• -19
• -5

Multiple Choice

If f(x) = 7, what is the value of x?

f(x) = 3x+1

• 2

• $$\frac{8}{3}$$

• 3

• 8

Slope Formula

Finding the Slope of a line given a graph or two points.

Slope & the
Coordinate Plane

Today we will be looking at types of slope and how to find slope from a graph, from a table and from two point using the slope formula, and from equations both standard and slope-intercept form.

​Dr. Tom Giles

You can use any two points on a line to find the slope

Types of slope

There are four main types of slope

=Positive Slope

=Negative Slope

=Zero Slope(y= line)

=Undefined Slope(x= line)

Multiple Choice

How many points do you need to find the slope of a line?

• 1

• 2

• 3

• 4

Multiple Choice

What type of slope is shown by the stairs in the image?

• positive

• negative

• undefined

• zero

Multiple Choice

What type of slope is shown in the image?

• Positive

• Negative

• Undefined

• Zero

Multiple Choice

What type of slope is Mario running in the picture?

• Positive

• Negative

• Undefined

• Zero

Step by Step:

• 1. Label the Points 1 and 2 (Slope is ALWAYS the same, no matter which point you pick to be the “first” or “second”.)

• 2. Label the X and Y for each point

• 3. Write the values in the slope formula

• 4. Simplify

Multiple Choice

What type of Slope?

• Positive

• Zero

• Negative

• Undefined

Practice

Find the slope of the line that goes through the points (5, 17) and (0,-3).

Step 1: Label the Points

• First Point ------> (X₁, Y₁) = (5, 17)

• Second Point ------> (X₂, Y₂) = (0, -3)

Multiple Choice

What type of Slope?

• positive slope

• negative slope

• undefined (no) slope

• zero slope

Step 2: Extract Values

• X₁ = 5 and Y₁ = 17

• X₂ = 0 and Y₂ = -3

Multiple Choice

What type of Slope?

• positive slope

• negative slope

• undefined (no) slope

• zero slope

Step 3: Plug the values into the slope formula.

-Remember that Y values go on top and X values go on bottom. 

-Make note of the MINUS in between each point for the top and bottom

-Don't mix the first (red) and second (blue) points. 

Multiple Choice

What is the slope in the picture?

• Positive
• Negative
• Zero
• Undefined

Step 4: Simplify

Solve for m using the Order of Operations (PEMDAS)

Make sure that you subtract the numbers correctly. Use a CALCULATOR!

**Remember- subtracting a negative number is the same as adding

Multiple Choice

What type of Slope?

• Negative

• Zero

• Undefined

• Positi

Multiple Choice

Find the slope of the line that goes through the points

(−11,−5) and (1,−12)

• $$-\frac{5}{8}$$

• $$\frac{16}{11}$$

• $$\frac{1}{6}$$

• $$-\frac{7}{12}$$

What does slope measure?

Multiple Choice

Find the slope of the line that goes through the points

(−1,−2) and (−3,−4).

• 1

• 2

• 3

• 4

Multiple Choice

When using a graph to find slope, which do you do first?

• Rise

• Run

Multiple Choice

The 'rise' part in rise/run tells us which way to go on which axis?

• y-axis

• x-axis

• coordinate plane

• y-intercept

Multiple Choice

What direction do you go when you are finding the rise?

• left and right

• up and down

Multiple Choice

The 'run' part in rise/run tells us which directions to go on the x-axis?

• up and down

• diagonal

• left and right

Multiple Choice

What is the slope of this line?

• 5/2

• 2/5

• -2/5

• -5/2

Multiple Choice

What is the slope of the line?

• 2/3

• -3/2

• 3/2

• -2/3

To find the slope of a line from a table

Multiple Choice

What is the slope?

• 3
• -3
• 10
• -6

Multiple Choice

Find the rate of change shown in the table.

• -1.5 cm/week

• 1.5 cm/week

• -1/5 cm/week

• 1/5 cm/week

Multiple Choice

Find the rate of change shown in the table.

• 3/125

• 125/3

• 500/12

• -3/125

Multiple Choice

Find the average rate of change shown in the table above.

• -3 degrees F every 2 hours.

• -1.5 degrees F every hour.

• 3 degrees F every 2 hours.

• 1.5 degrees F every hour.

Finding slope from two point:

Multiple Choice

Determine the slope.

• m=1/7
• m=-1/7
• m=-7
• m=7

Multiple Choice

Find the slope of the line that passes through:
(-3, -4) and (7, 6)

• 0
• Undefined
• -1
• 1

Multiple Choice

Find the slope of the line that passes through:
(-12, -5) and (0, -8)

• 1/4
• -1/4
• 4
• -4

Multiple Choice

Find the slope of the line that passes through:
(10, 1) and (5, 2)

• 1/5
• -1/5
• 5
• -5

Identifying Slope from an Equation

Slope intercept form of an equation: y=mx+b

m=slope

b=y-intercept

Slope is always attached to the x value when in slope intercept form of a line

Multiple Choice

What does "m" represent in y=mx+b?

• y-intercept
• slope
• macaroni
• nothing

Multiple Choice

What is the slope in the equation:  y=4x+3

• 3
• 4x
• 4
• x

Multiple Choice

Which of these represents slope-intercept form?

• y - y₁ = m(x-x₁)

• Ax + By = C

• y = mx + b

Multiple Choice

What is the slope of the line with the equation
$$y\ =\ -\frac{3}{2}x\ +\ 4$$  

• $$-\frac{3}{2}$$  

• $$\frac{3}{2}$$  

• $$4$$  

• $$-4$$  

Multiple Choice

What is the slope in the equation y=2x + 3?

• 2
• 3
• 5
• Cannot be Determined 

Parallel Lines

Parallel lines are lines that have the exact same slope but different y-intercepts.

If the y-intercepts were the same, you would have the exact same line not parallel lines.

Multiple Choice

The slopes of parallel lines are...

• the same

• opposite

• always different

Multiple Choice

What slope is parallel to:  
m = ³/₄

• ⁴/₃
• ³/₄
• ^-3/₄
• ^-4/₃

Multiple Choice

Which line is parallel to
y = 2x - 7  ?

• y = -2x + 8
• y = ¹/₂x - 7 
• y = ^-1/₂x + 2
• y = 2x - 3 

Multiple Choice

y = 3x +2
y = 3x - 3
These lines are...

• Parallel
• Perpendicular
• Neither
• The same line

Perpendicular Lines

Perpendicular lines are lines that have slopes that are opposite recipricols of each other.

- opposite - signs change

- recipriols - position of the numbers change

ex: 3 and -1/3 are perpendicular slopes

Multiple Choice

Slopes of perpendicular lines are...

• opposite reciprocals.
• opposites.
• the same.
• always 7.

Multiple Choice

What is the slope of a line perpendicular to a line with slope ^-6/₅ ?

• ^-6/₅
• ^-5/6
• ⁵/₆
• ^-4/₃

Multiple Choice

Which line is perpendicular to
y = 2x - 7  ?

• y = -2x + 8
• y = ¹/₂x - 7 
• y = ^-1/₂x + 2
• y = 2x - 3 

Multiple Choice

y = ^{- 2}/₃x + 2
y = ³/₂x + 9
These lines are...

• Parallel
• Perpendicular
• Neither

Graphing Coordinate Points

​Coordinate Plane

​The coordinate plane is a two - dimensional plane formed by the intersection of the x-axis (horizontal axis) and the y-axis (vertical axis)

​

​The point where the the x-axis and y-axis intersect is referred to as the origin.

​Quadrants

​When the x-axis and y-axis intersect, they form 4 quadrants.

​

​

​Points in the Coordinate Plane

​The points in each of the 4 quadrants are identified using and ordered pair consisting of an x-coordinate and y - coordinate (x,y).

​

​Points in the Coordinate Plane

The x-coordinate represents the horizontal distance from the origin and the y-coordinate represents vertical distance from the origin.

​

Hotspot

Which line is the X-AXIS?

Multiple Choice

What is the axis of symmetry for

2x² - 20x + 7 = 0

hint: x = -b/2a

• x = -5

• x = 7/2

• x = 5

• x = -20

Hotspot

Which line is the Y-AXIS?

Graphing a Point

Always written in the form (x,y)

​

The x-value tells us to

move left or right

​

The y-value tells us to

move up or down

​

Graph (4,6)​

​

Graphing a Point

Coordinate pairs are listed (x, y). X tells you how far left (negative) or right (positive) you go from the origin. Y tells you how far up (positive) or down (negative) you go from the origin.

(-2, 3) - move 2 left and up 3

(0, -3.5) - don't move over, and go down 3.5

Cartesian Coordinates

We represent points on a cartesian plane with coordinates. The x-axis coordinate is always the first number listed.

Graphing on a Coordinate Plane

Labelling

Label the quadrants in the grid shown.

Drag labels to their correct position on the image

I

III

IV

II

Labelling

Identify the general form of coordinates found in each quadrant.

Drag labels to their correct position on the image

(+,-)

(-,-)

(+,+)

(-,+)

Fill in the Blank

What is the coordinate pair that represents point A?

(

-

,

)

Labelling

Identify the coordinates of each point plotted.

Drag labels to their correct position on the image

(-1,6)

(4,3)

(3,4)

(-5,-8)

(6,-1)

(-8,-5)

(-2,7)

(7,-2)

Graphing

Plot the following points on the grid shown.

(-6,4)
(5,1)
(0,-7)
(2,-3)

Graphing

Plot the points on the grid shown.

(-3,5)
(9,-5)

(-10,0)

(7,2)

Labelling

Identify the coordinates of each point graphed.

Drag labels to their correct position on the image

(-5,4)

(4,-5)

(8,0)

(-1,-3)

(5,-6)

(-6,5)

(-3,-1)

(0,8)

Labelling

Identify the coordinates of each point graphed.

Drag labels to their correct position on the image

(2,5)

(9,7)

(-2,-5)

(9,-1)

(-7,9)

(-9,-1)

(6,-8)

(7,9)

(6,8)

Fill in the Blank

What is the coordinate pair that represents point D?

(

,

)

Fill in the Blank

What is the coordinate pair that represents point B?

Fill in the Blank

What is the coordinate pair that represents point E?

Fill in the Blank

What is the coordinate pair that represents point K?

Fill in the Blank

What is the coordinate pair that represents point H?

Draw

Plot a point at (3,8) on the grid. Label the point A.

But for our purposes for the ACT, when graphing Inequalities -

Use Desmos

Draw

Plot a point at (-7,-2) on the grid. Label the point B.

Draw

Plot a point at (3,-5) on the grid. Label the point C.

Draw

Plot a point at (-4,9) on the grid. Label the point D.