Exercise 12 Page 229

a We are asked to write equations in slope-intercept form to represent the cost

y

to attend the fitness centers for

x

months.

y = m x + b

Let's see what the slope

m

and the intercept

b

mean in this context.

Fitness Center	slope $m$ (monthly fee in dollars)	intercept $b$ (membership fee in dollars)	Equation
Fit-N-Trim	$80$	$0$	$y = 80 x$
Fit-For-Life	$55$	$75$	$y = 55 x + 75$

Let's graph these equations. Use the intercept as a starting point and the slope to work out the direction.

b We can see from the graph that the lines intersect at

(3, 240) .

Parallel lines do not intersect, so the graphs are not parallel.

Note that we can also arrive at the same conclusion by investigating the slopes instead of the graphs. The slope of these lines are $m_{1} = 80$ and $m_{2} = 55 .$ These are not equal, so the lines are not parallel.

c Let's investigate the relative position of the two lines and see what this position means in the context of the question.

The variable $y$ represents the cost to attend the fitness centers for $x$ months.

Since $(3, 240)$ is on both lines, the cost of a three month membership is $240$ dollars in both centers.
For $x < 3,$ the blue line is below the red line, so for a membership shorter than three month the Fit-N-Trim center is more economical.
For $x > 3,$ the blue line is above the red line, so for a membership longer than three month the Fit-For-Life center is more economical.