Question

Kevin needs to lease out a music studio to record his new album. The studio charges an initial studio-use fee plus an hourly fee for each hour in the studio. The total amount of money Kevin would have to pay to use the studio for tt hours can be determined using the equation P, equals, 100, plus, 50, t, .P=100+50t. What is the yy-intercept of the equation and what is its interpretation in the context of the problem?

Answer 1

In the equation

�

=

100

+

50

�

P=100+50t,

�

P represents the total cost Kevin would have to pay, and

�

t represents the number of hours he spends in the studio.

The

�

y-intercept of an equation is the point at which the graph intersects the

�

y-axis. In this case, the

�

y-intercept occurs when

�

=

0

t=0, meaning it represents the initial amount Kevin has to pay when he hasn't spent any hours in the studio (

�

=

0

t=0).

Let's substitute

�

=

0

t=0 into the equation:

�

=

100

+

50

×

0

P=100+50×0

�

=

100

P=100

So, the

�

y-intercept is

(

0

,

100

)

(0,100).

In the context of the problem, the

�

y-intercept (100) represents the initial studio-use fee that Kevin has to pay when he hasn't spent any time in the studio. In other words, even if Kevin doesn't use the studio (

�

=

0

t=0), he still has to pay an initial fee of $100. This could be considered a setup fee or a fee for reserving the studio space before any recording time is used.

Explanation: