Interpreting Graphs of Proportional Relationships

Student Summary

For the relationship represented in this table, yy is proportional to xx. We can see in this table that 54\frac54 is the constant of proportionality because it’s the yy value when xx is 1.

The equation y=54xy = \frac54 x also represents this relationship.

  xx     yy  
4 5
5 254\frac{25}{4}
8 10
1 54\frac{5}{4}

Here is the graph of this relationship.

Graph of a line, x y plane, origin O.
Graph of a lin, x y plane, origin O. Horizontal and vertical axis scale 0 to 10 by 1’s. Line starts at (0 comma 0), rises to point (1 comma the fraction 5 over 4), rises to point (4 comma 5), rises to point (5 comma the fraction 25 over 4), then rises to point (8 comma 10) and keeps rising.

If yy represents the distance in feet that a snail crawls in xx minutes, then the point (4,5)(4, 5) tells us that the snail can crawl 5 feet in 4 minutes.

If yy represents the cups of yogurt and xx represents the teaspoons of cinnamon in a recipe for fruit dip, then the point (4,5)(4, 5) tells us that you can mix 4 teaspoons of cinnamon with 5 cups of yogurt to make this fruit dip.

We can find the constant of proportionality by looking at the graph: 54\frac54 is the yy-coordinate of the point on the graph where the xx-coordinate is 1. This could mean the snail is traveling 54\frac54 feet per minute or that the recipe calls for 1141\frac14 cups of yogurt for every teaspoon of cinnamon.

In general, when yy is proportional to xx, the corresponding constant of proportionality is the yy-value when x=1x=1

Visual / Anchor Chart

Standards

Addressing
7.RP.A

7.RP.A

7.RP.2.b

7.RP.2.d

7.RP.A.2.b

7.RP.A.2.d

7.RP.2.d

7.RP.A.2.d