Lesson 6: Direct Variation

Direct Variation

No y-intercept required

​Direct Variation

​Direct variation is represented by the formula y = kx and y is said to vary directly with x. You can graph direct variations the same way you graph linear equations. Direct variations have a y-intercept of zero.

​Modelling Direct Variation

​Any time you see, in a word problem, that one factor varies directly with another factor, then you can assume there is a direct variation at play. This means that the formula y = kx should be used. When given two values that are related, then you plug in the values and find k.

​Sample Problem

​Hailstones form when strong updrafts support ice particles high in clouds, where water droplets freeze onto the particles. Given two different hailstones, one with a diameter of 0.75 inches formed in 12 minutes and one with an unknown diameter formed at 20 minutes. Assuming that the diameter varies directly with time, do the following...

​1. Write an equation that shows the direct variation using d for diameter and t for time.

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​2. Predict the diameter of the hailstone formed at 20 minutes.

​Finding Direct Variation

​When given a table of values and asked to determine whether the table depicts a direct variation, we divide the y value by the x value and see if the entire table gives the same quotient each time as shown in the table to the right.

Multiple Choice

Direct variation uses the following form:

• y=kx

• y=(x-h)²+k

• y=mx+b

• y=ax²+bx+c

Multiple Choice

True or False:

Every direct variation has a non-zero y-intercept.

• True

• False

Multiple Choice

Given the following points, determine whether x and y vary directly:

(2, 6) (3, 9) (4, 12) (5, 15)

• They do vary directly

• They do not vary directly