Practice Proportional Line in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A straight line that passes through the origin, representing a proportional relationship of the form y=kxy = kx with constant ratio kk.

When x=0x = 0, y=0y = 0. The line passes through the origin—no head start.

Showing a random 20 of 50 problems.

Example 1

hard
A graph shows a line passing through (0,0)(0,0), (4,10)(4,10), and a third point (x,25)(x,25). Find xx.

Example 2

hard
On a proportional line, the point (a,12)(a,12) and the point (3,4)(3,4) both lie on the line. Find aa.

Example 3

medium
Is the table (1,3),(2,5),(3,7)(1,3),(2,5),(3,7) proportional?

Example 4

easy
If y=8xy=8x, find yy when x=5x=5.

Example 5

hard
Graph y=3xy=3x. Identify a third lattice point on the line besides (0,0)(0,0) and (1,3)(1,3).

Example 6

easy
A proportional line passes through (2,10)(2,10). Find kk.

Example 7

medium
Three of the points lie on the same proportional line: (2,8),(3,12),(5,21)(2,8),(3,12),(5,21). Which one does NOT?

Example 8

challenge
A line is proportional and also passes through (2,5)(2,5). A student claims it also passes through (4,9)(4,9). Verify and correct.

Example 9

easy
What is the yy-intercept of any proportional line y=kxy=kx?

Example 10

easy
Write the equation of a proportional line with constant 6.

Example 11

medium
What is the slope of the proportional line y=−2xy=-2x?

Example 12

medium
A car travels at a constant 6060 km/hr. Write dd as a proportional function of tt and find dd when t=2.5t=2.5 hr.

Example 13

medium
Is y=x4y=\tfrac{x}{4} a proportional line? If yes, give kk.

Example 14

medium
The graph of y=kxy=kx passes through (4,10)(4,10). Find kk and then yy at x=6x=6.

Example 15

hard
Is xy=12xy=12 a proportional relationship between xx and yy?

Example 16

medium
A recipe uses 2 cups of flour per 3 cookies. Write the proportional model and find flour for 12 cookies.

Example 17

hard
The cost CC to print flyers is proportional to the number nn printed. 200200 flyers cost $30. Write C(n)C(n) and find the cost of 750750 flyers.

Example 18

easy
Does the line y=5xy=5x pass through the origin?

Example 19

easy
If y=4xy=4x, find yy when x=3x=3.

Example 20

medium
A proportional graph passes through (6,9)(6,9). What is yy when x=10x=10?
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