Direct Variation

You buy cashews at the bulk food store and the cost is $2 per 100g. The following logic would apply-

If you doubled the amount of cashews the cost would double; if you halved the amount of cashews, the cost would be halved. This is called a direct variation where the cost varies directly with the weight of the cashews.

You may graph this relationship and the result will be-

Equation-

x (g)	200	400	600	800
y ($)	4	8	12	16

Graph-

Note that (0,0) is on the graph as there is no cost for cashews. Also note that the slope can be calculated by-

In general a direct variation yields the equation y = mx where any point (other than 0,0) yields the slope-

Ex1

Given the following data, determine the constant of variation

x	3	5	7	9
y	9	15	21	27

Ex2

If y varies directly as x, and y is 10 when x is 2, determine the value of x when y is 35

Calculation	Comment
	m stays the same throught (constant)
x 2 ? y 10 35	Organize in a table
	Substitute
10x = 35(2) 10x = 70 x = 7	Cross multiply

 

Ex3

The time it takes to get to a destination varies directly with the distance. If you drove 450 km in 5 hours. How long would it take to drive 200 km?

d	450	200
t	5	t