Exercise 40 Page 214

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

y=mx

SubstituteII

x= 4, y= - 2

- 2=m( 4)

DivEqn

.LHS /4.=.RHS /4.

- 2/4=m

▼

Simplify left-hand side

ReduceFrac

a/b=.a /2./.b /2.

- 1/2=m

MoveNegNumToFrac

Put minus sign in front of fraction

-1/2=m

RearrangeEqn

Rearrange equation

m=-1/2

Now that we have the constant of variation, we can write the function. y=-1/2x With this equation, we can find any value of x or y when we are given the other. In this case, we are looking for y when x=7.

y=-1/2x

Substitute

x= 7

y=-1/2( 7)

MoveRightFacToNumOne

1/b* a = a/b

y=-7/2

For the equation y=- 12x, when x=7, the value of y is - 72.