Constant of Proportionality

Definition & Basics

100

What is the constant of proportionality?

The constant ratio between two proportional quantities.

200

If y = 5x, what is the constant of proportionality?

5

300

In a proportional relationship, what does the graph always pass through?

The origin (0,0).

400

If y = kx, what does “k” represent?

The constant of proportionality.

500

If y/x = 9 for all values of x and y, what is the constant of proportionality?

9

Tables

100

Find k:
x = 1, 2, 3
y = 4, 8, 12

4

200

Find k:
x = 20, 40,60
y =  5, 10, 15

1/4

300

Find k:
x = 2, 4, 6
y = 10, 20, 30

5

400

Write the equation:
x = 12, 24, 36
y =  3, 6, 9

y = 1/4x or y = 0.25x

500

Write the equation: 

x = 8, 12, 16  
y = 20, 30, 40

y = 2.5x

Graphs

100

If a line passes through (0,0) and (2,6), what is k?

3

200

If a line passes through (0,0) and (4,10), what is k?

2.5

300

If a line passes through (0,0) and (15, 5), what is k?

1/3

400

If a line passes through (0,0) and (10,25), what is the equation that relates x and y?

y = 2.5x

500

If a line passes through (0,0) and (28, 7), what is the equation that relates x and y?

y = 1/4x or y = 0.25x

Word Problems

100

A car travels 180 miles in 3 hours. What is the constant of proportionality?

60

200

A recipe uses 2 cups of sugar for every 5 cups of flour. What is the constant of proportionality (sugar per flour)?

0.4

300

A machine produces 270 cars in 3 months. What is k?

90

400

A runner covers 12 miles in 1.5 hours. What is the equation that relates the number of miles run, y, to the hours, x?

y = 8x

500

A faucet fills 14 gallons in 3.5 minutes. What is the equation that relates the number of gallons filled, y, to the minutes, x?

y = 4x

Mixed Challenge

100

If y = 3x + 1, is this a proportional relationship? Explain.

No, because of the +1; it does not pass through the origin.

200

If y = 0.75x, what is the constant of proportionality, and what does it represent if y is cost and x is pounds of fruit?

k = 0.75; it represents $0.75 per pound.

300

If y varies directly with x and y = 18 when x = 6, find y when x = 15.

k = 3, so y = 45

400

Two quantities are proportional. When x = 8, y = 20. Write the equation and find y when x = 50

k = 2.5, equation y = 2.5x, so y = 125.

500

A graph passes through (0,0) and (12,30). Another line passes through (0,0) and (8,20). Are these relationships proportional to each other? Explain.

Yes, both have the same constant of proportionality (k = 2.5), so they represent the same proportional relationship.