8.16 Linear Equations

Pre-Algebra

SOL 8.15 and 8.16

SOL Prep

Multiple Choice

Which set of elements can replace the missing values and the relation remain a function?

Multiple Choice

Consider the coordinate grid. What is the range of the set of points?

• $$\left\{(-3,-1),(-2,-2),(1,1),(2,2),(3,3)\right\}$$

• $$\left\{-3,-2,-1,1,2,3\right\}$$

• $$\left\{-2,-1,1,2,3\right\}$$

• $$\left\{-3,3\right\}$$

Slope

Topics in this quizizz:

- Identifying slope (direction)

- Finding slope of a line (steepness)

- Slope from a Table

- Slope from an Equation

Identifying Slope of a Line

• Slope can tell us the direction of the line!

• Refresh yourself of the 4 types of slope using the picture to the right:

Identifying Basic Slopes

Slope: the 'steepness' of a line.

​

There are FOUR basic categories for SLOPES

POSITIVE SLOPE

NEGATIVE SLOPE

SLOPE OF ZERO

UNDEFINED SLOPE

Match

Match the Graph with its slope.

Negative

Positive

Zero

Undefined

• Negative

• Positive

• Zero

• Undefined

Multiple Choice

What type of slope?

• positive

• negative

• zero

• undefined

Multiple Choice

What type of slope?

• negative

• steep

• undefined

• zero slope

Multiple Choice

What type of slope?

• zero slope

• undefined

• negative

• positive

Multiple Choice

What type of slope?

• undefined

• positive slope

• negative slope

• zero slope

Finding the Slope of a Line

• Slope can tell us how steep a line is!

• Each line can be assigned a value (a #) that tells us how steep the line is.

• Slope is written as a ratio (rise/run)

• Always make sure to simplify your answer!

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{2}{3}$$

• $$\frac{3}{2}$$

• 3

• $$\frac{1}{3}$$

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{1}{2}$$  

• $$\frac{2}{1}$$  

• 2

• 1

Multiple Choice

Find the slope of the line below using rise/run.

• 3

• $$\frac{1}{3}$$  

• 2

• 1

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{5}{3}$$  

• $$\frac{3}{5}$$  

• 5

• $$\frac{5}{4}$$  

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{1}{2}$$  

• $$\frac{4}{2}$$  

• 2

• 3

• $$\frac{2}{3}$$  

Multiple Choice

Given the graph, identify the slope (m) and y-intercept (b) of the function.

• Slope of $$-\frac{1}{2}$$ and y-intercept of $$-1$$

• Slope of $$\frac{1}{2}$$ and y-intercept of $$1$$

• Slope of $$2$$ and

  y-intercept of $$1$$

• Slope of $$2$$ and

  y-intercept of $$-1$$

Multiple Choice

What is the apparent slope of the line?

• $$-\frac{5}{2}$$

• $$-\frac{2}{5}$$

• $$\frac{2}{5}$$

• $$\frac{5}{2}$$

Multiple Choice

Which line appears to be a graph of the equation shown? $$y=-2x-1$$  

Finding slope from a Table

• Slope = change in y/change in x

• Use the table to find the value the y is changing by. That is the numerator!

• Use the table to find the value the x is changing by. That is the denominator!

• ANOTHER OPTION: Graph the points and count rise/run

Multiple Choice

Find the slope. Simplify, if you can.

• $$\frac{2}{5}$$

• $$\frac{5}{2}$$

• $$2\ \frac{1}{2}$$

• 2

Multiple Choice

Find the slope. Simplify, if you can.

• $$\frac{1}{2}$$  

• $$\frac{4}{8}$$  

• 4

• 2

Multiple Choice

Find the slope. Simplify, if you can.

• 3

•   $$\frac{1}{3}$$  

• $$-\frac{1}{3}$$  

• -3

Multiple Choice

Analyze the values for a linear function given in the table. Identify the slope and y-intercept for the function.

• slope = -3 and

  y-intercept = 0

• slope = 0 and

  y-intercept = -3

• slope = 2 and

  y-intercept = -3

• slope = 2 and

  y-intercept = 1

Multiple Choice

Which rule does the table represent?

• $$y=2x+3$$

• $$y=2x-3$$

• $$y=\frac{1}{2}x+3$$

• $$y=\frac{1}{2}x-3$$

Slope from an equation

• The number in front of the x in the equation is the slope!

Multiple Choice

Identify the slope in the equation:

$$y=8x$$  

• 8

• 1/8

• -8

• 0

Multiple Choice

Identify the slope in the equation:

$$y=\frac{5}{6}x$$  

• $$\frac{5}{6}$$  

• $$\frac{6}{5}$$  

• 5

• 6

Dependent Variable vs Independent Variables

Example:

Sarah is participating in a walkathon to raise money for local literacy programs. The amount of money Sarah will raise depends on the distance she walks.

m = the amount of money Sarah will raise (DEPENDENT)

d = the distance Sarah walks (INDEPENDENT)

Multiple Choice

Maggie opened a savings account and deposited $200. She will deposit $50 into this account each week, w, and will make no withdrawals. The equation below shows how she will calculate the total amount in the account, t, after each deposit.

Which of the following is the dependent variable? $$t=50w+200$$  

• $$t$$  

• $50

• $$w$$  

• $200

Multiple Choice

Identify the dependent variable:

The cost of apples (c), and the number of pounds you buy (p)

• p = dependent

• c = dependent

Multiple Choice

Name the DEPENDENT variable from the table below.

• minutes

• bubbles

Multiple Choice

Name the INDEPENDENT variable from the table below.

• words

• minutes

Multiple Choice

Carey and Justin are raising money to purchase books for their school's library. The more money they raise, the more books they will be able to purchase for the library.

m = the amount of money Carey and Justin raise

b = the number of books Carey and Justin will be able to purchase

Which of the variables is dependent?

• m

• b

Multiple Choice

Sarah is bringing treats to her elementary school class on her birthday. The number of treats she brings in is based on the number of students in her class.

t = the number of treats

s = the number of students

Which of the variables is independent?

• s

• t

Multiple Choice

Sophie earned $1 for every she got an A on her report card.

m = money

A = A on report card

The dependent variable is:

• m = money

• A = A on report card

Multiple Choice

A movie ticket is $8.50 per person. What is the independent variable?

• Cost

• Number of people

• Time

• Cinema