Proportional Relationships y = mx

What you'll learn

Recognize proportional relationships in tables, graphs, and equations
Find the constant of proportionality m
Write and use an equation of the form y equals m times x

Words to know

Proportional relationship —: a relationship where two quantities have a constant ratio
Constant of proportionality —: the steady multiplier m in y equals m times x
Origin —: the point (0, 0) where a proportional graph begins
Unit rate —: the value of y when x is 1
Linear —: forming a straight line when graphed

Why it matters Many real situations, such as pay per hour or distance at a steady speed, follow y equals m times x, so finding m lets us predict any value.

Worked examples

Model ItI do

A table shows that 2 hours of work earns 30 dollars. Write the equation y equals m times x.

Find m as the unit rate: 30 divided by 2 = 15 dollars per hour. So the equation is y equals 15 times x.

Try It TogetherWe do

For the equation y equals 4 times x, find y when x is 6.

Substitute 6 for x: y equals 4 times 6, which is 24. So y is 24.

Now YouYou do

A car travels 180 miles in 3 hours at a steady speed. Write the equation y equals m times x for distance y and time x.

Find the constant m by dividing distance by time. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

1.For y equals 3 times x, find y when x is 4.
2.Find m if y is 20 when x is 5.
3.Does the graph of a proportional relationship pass through the origin?

On Level

The core Quick Check from the book.

1.For y equals 5 times x, find y when x is 3.
2.Find m if y is 24 when x is 4.
3.Does the graph of a proportional relationship pass through the origin?
4.For y equals 2 times x, find y when x is 10.
5.A worker earns 45 dollars in 5 hours. Find the constant of proportionality.

Challenge

Stretch your thinking.

1.A table shows 3 hours of work earns 51 dollars. Write the equation y equals m times x, then find the pay for 7 hours.
2.A graph of a proportional relationship passes through the point (4, 10). What is the constant of proportionality?
3.For y equals 6 times x, find x when y is 42.