y = mx

y = mx

Proportional Relationship

Direct variation

Slope Intro Review

 $slope\ =\ m\ =\frac{rise}{run\ }$  

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Categorize the slope of the line

• Positive

• Negative

• Zero

• Undefined

Fill in the Blanks

What is the rise?

Fill in the Blanks

What is the run?

Multiple Choice

What is the slope of the line?

• -2/3

• 2/3

• 3/2

• -3/2

Fill in the Blanks

What is the rise?

Fill in the Blanks

What is the run?

Multiple Choice

What is the slope of the line?

• 3/1

• -3/1

• 1/3

• -1/3

Direct Variation

y = mx

If you can multiply the x values by the same constant and get the y value there is a direct variation. (This is also proportional)

Fill in the Blanks

How much money is raised every hour?

Fill in the Blanks

How much money is raised in three hours?

Direct Variation Table

y directly varies in relation to x

y = mx
where m is a constant we multiply by x to get y

 $\frac{y}{x}=m\ \ \ \ \frac{6}{3}=2\ \ \ \ \ \frac{10}{5}=2\ \ \ \ m=2$  

Multiple Choice

Proportional or Non-Proportional?

• Proportional

• Non-Proportional

Multiple Choice

 $\frac{14}{7}\ =\ \frac{32}{8}$  

• True

• False

Multiple Choice

Does the table represent a proportional relationship?

• Yes.
• No.

Direct Variation

Graph

When data has a direct variation you get a straight line (linear) that goes through the origin.

Multiple Choice

The graph shown is:

• Proportional

• Not Proportional

Multiple Choice

Is the graph proportional or nonproportional?

• Proportional

• Non Proportional

Multiple Choice

Is the graph proportional or non proportional?

• proportional because it is a straight line and goes through the origin

• non proportional because it is not a straight line but goes through origin

• non proportional because it does not go through the origin but is a straight line

• non proportional because it does not go through the origin and is not a straight line

Equation

In the table to the right if we take y divided by x we get 5.

 $\frac{-5}{-1}\ =\ \frac{10}{2}\ =\ 5$  

therefore, m = 5
Our equation is
y = mx
y = 5x

Multiple Choice

What is the slope of the table?

• 1/4

• 4

• -6

• -4

Multiple Choice

What is the slope of the table?

• 1/2

• 2

• -2

• 3

Multiple Choice

What equation is represented by the table?

• y = 1/8x

• y = 8x

• y = x - 8

• y = x - 21

Multiple Choice

What equation is represented by the table?

• y = 1/3x

• y = 3x

• y = 10x

• y = x - 1/3

Multiple Choice

Find the slope

• -3/4
• 4/3
• 3/4
• -4/3

Multiple Choice

Find the slope

• 4/5
• 5/4
• -5/4
• -4/5

Fill in the Blanks

Solve 4x + 3 when x = 5