Exercise 31 Page 305

Functions where y varies directly with x — direct variation equations — follow a specific format. y= mx In this form, m≠ 0. From the exercise, we know that y is 14 when x is -5. By substituting the given values for x and y into the equation, we can determine the constant of variation, m.

y=mx

SubstituteII

y= - 5, x= 1/4

- 5 =m( 1/4)

MultEqn

LHS * 4=RHS* 4

- 20 = m

RearrangeEqn

Rearrange equation

m=- 20

Now that we have the constant of variation, we can write the function. y= - 20x The graph of a direct variation equation is a line which passes through the point (0,0) and has a slope m, which in our case is - 20. m=rise/run=-20/1 This means that if we go 1 step to the right, the y value of the function decreases by 20.