Exercise 33 Page 305

Functions where y varies directly with x — direct variation equations — follow a specific format. y= mx In this form, m≠ 0. We have been given that y is 7.2 when x is 1.2. By substituting the given values for x and y into the equation, we can determine the constant of variation, m.

y=mx

SubstituteII

y= 7.2, x= 1.2

7.2=m* 1.2

DivEqn

.LHS /1.2.=.RHS /1.2.

7.2/1.2=m

CalcQuot

Calculate quotient

6=m

RearrangeEqn

Rearrange equation

m=6

Now we can write the direct variation equation that relates x and y. y= 6x The graph of a direct variation equation is a line which passes through the origin and has a slope m, which in our case is 6. m=rise/run=6/1 This means that if we go 1 step to the right, the y value of the function increases by 6.