Objective

I understand the information given by graphs of proportional relationships that are made of up of points or a line.

I can find the constant of proportionality from a graph.

I can draw the graph of a proportional relationship given a single point on the graph (other than the origin).

Online Workbook

Take me to the website.

Llévame al sitio web.

Lesson Summary

For the relationship represented in this table, y is proportional to x. We can see in the table that $LaTeX: \frac{5}{4}$ is the constant of proportionality because it’s the y value when x is 1.

The equation $LaTeX: y=\frac{5}{4}x$ also represents this relationship.

x	y
4	5
5	$LaTeX: \frac{25}{4}$
8	10
1	$LaTeX: \frac{5}{4}$

Here is the graph of this relationship.

A line is graphed in the coordinate plane with the origin labeled “O”. The numbers 0 through 10 are indicated on the x axis. The numbers 0 through 10 are indicated on they axis. The line begins at the origin. It moves steadily upward and to the right passing through the points with coordinates 1 comma five-fourths, 4 comma 5, 5 comma 25 fourths, and 8 comma 10.

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

If y represents the cups of yogurt and x represents the teaspoons of cinnamon in a recipe for fruit dip, then the point (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, because $LaTeX: \frac{5}{4}$ is the y-coordinate of the point on the graph where the x-coordinate is 1. This could mean the snail is traveling $LaTeX: \frac{5}{4}$ feet per minute or that the recipe calls for $LaTeX: 1\frac{1}{4}$ cups of yogurt for every teaspoon of cinnamon.

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

Additional Practice on Khan Academy

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