Exercise 32 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 65 when x is - 56. By substituting the given values for x and y into the equation, we can determine the constant of variation, m.

y=mx

SubstituteII

x= -5/6, y= 6/5

6/5=m( -5/6)

DivEqn

.LHS /(-5/6).=.RHS /(-5/6).

6/5/(-5/6)=m

DivFracByFracSL

.a/b /c/d.=a/b*d/c

-36/25=m

RearrangeEqn

Rearrange equation

m=-36/25

Now we can write the direct variation equation that relates x and y. y= -36/25x 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 - 3625. m=rise/run=-36/25 This slope means that line descends vertically by - 36 step for every 25 steps to the right.