Question

Linear model function

Answer 1

Using equations of linear model function, the number of hours Jeremy wants to skate is calculated as 3.

How to Write the Equation of a Linear Model Function?

The equation that can represent a linear model function is, y = mx + b, where m is the unit rate and b is the initial value.

Equation for Rink A:

Unit rate (m) = (35 - 19)/(5 - 1) = 16/4 = 4

Substitute (x, y) = (1, 19) and m = 4 into y = mx + b to find b:

19 = 4(1) + b

19 - 4 = b

b = 15

Substitute m = 4 and b = 15 into y = mx + b:

y = 4x + 15 [equation for Rink A]

Equation for Rink B:

Unit rate (m) = (39 - 15)/(5 - 1) = 24/4 = 6

Substitute (x, y) = (1, 15) and m = 6 into y = mx + b to find b:

15 = 6(1) + b

15 - 6 = b

b = 9

Substitute m = 6 and b = 9 into y = mx + b:

y = 6x + 9 [equation for Rink B]

To find how many hours (x) both would cost the same (y), make both equation equal to each other

4x + 15 = 6x + 9

4x - 6x = -15 + 9

-2x = -6

x = 3

The hours Jeremy wants to skate is 3.

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