Proportional Relationships Graphed

a linear relationship that intersects the origin

• rate of change

• equivalent ratios

• intercepts

• slope

• proportional

Answer explanation

Quantities are proportional if they have a constant ratio. When we graph a proportional relationship produces a straight line that intersects the origin.

The rate of change is how one quantity changes in relation another, and that relationship may or may not be proportional. If the rate of change is constant, a straight line will be produced when graphed, but the line will only intersect the origin if the relationship is also proportional. The slope is equal to the rate of change. x- and y-intercepts occur for straight lines as well as other relationships.

a relationship that produces a straight line when graphed

• rate of change

• equivalent ratios

• axis

• slope

• linear

Answer explanation

A linear relationship produces a straight line when graphed. The rate of change is how one quantity changes in relation another. If the rate of change is constant, a straight line will be produced when graphed, but the rate of change of some relationships are not constant, so will not produce a straight line. The slope is equal to the rate of change, so will only produce a straight line when it is constant. An axis is a number line in a coordinate system.

What is the rate of change for the following graph?

• 80

• 20

• 40

• 160

• 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

Which graph is proportional?

• A

• B

• C and A

• All of the graphs are proportional

Find the rate of change

• 1

• 2

• 11

• Not a constant slope/Non-Linear

Find the rate of change

• 1

• 2

• 11

• Not a constant slope/Non-Linear

Which graph shows a proportional relationship between x and y?

• F

• G

• H

• J

Which line shows a proportional relationship between x and y?

• Line L

• Line M

Find the rate of change

• 3

• -3

• 20

• Not a constant slope/Non-Linear