Exercise 46 Page 306

Functions where y varies directly with x — direct variation equations — follow a specific format. y= mx In this form, m≠ 0. We can substitute the x- and y-values from the known point, ( - 5, 3), into this equation to determine the constant of variation, m.

y=mx

SubstituteII

x= - 5, y= 3

3=m ( - 5)

DivEqn

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

3/- 5=m

MoveNegDenomToFrac

Put minus sign in front of fraction

- 3/5=m

RearrangeEqn

Rearrange equation

m=- 3/5

Now that we have the constant of variation, we can write the function. y= - 3/5x 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 x when y=- 4.8.

y=- 3/5x

Substitute

y= - 4.8

- 4.8=- 3/5x

MoveNegFracToNum

Put minus sign in numerator

- 4.8=- 3x/5

MultEqn

LHS * 5=RHS* 5

- 24 =- 3x

DivEqn

.LHS /(- 3).=.RHS /(- 3).

8 = x

RearrangeEqn

Rearrange equation

x = 8

The missing value is 8.