Exercise 30 Page 305

Functions where y varies directly with x — direct variation equations — follow a specific format. y= mx In this form, m≠ 0. We know that y is 12 when x is 3. By substituting the given values for x and y into the equation, we can determine the constant of variation, m.

y=mx

SubstituteII

y= 1/2, x= 3

1/2=m* 3

DivEqn

.LHS /3.=.RHS /3.

12/3=m

DivFracD

a/c/b= a/b* c

1/6=m

RearrangeEqn

Rearrange equation

m=1/6

Now we can write the direct variation equation that relates x and y. y= 1/6x 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 16. m=rise/run=1/6 This slope means that line rises vertically by 1 step for every 6 steps to the right.