Exercise 30 Page 170

Practice makes perfect

a To write the linear model we will use the slope-intercept form of a line, where m is the slope and b is the y-intercept.

y= mx+ b

In the model y represents the total cost and x represents the number of hours of studio time. Since the recording fee is hourly, 75 dollars is the slope. y= 75x+b The initial fee for an album is 50 dollars. This is the cost y when x=0. Therefore, it is the y-intercept of the function. y=75x+ 50

b In order to decide whether purchasing 12 hours recording time at the studio or buying a $750 music software program is less expensive, we will evaluate the function for x= 12.

y=75x+50

Substitute

x= 12

y=75( 12)+50

Multiply

y=900+50

AddTerms

Add terms

y=950

It would cost $950 to use the recording studio for 12 hours. Therefore, it is less expensive to purchase the $750 music software program.