Question

Terry brings home $14 per hour he works. When he started this job, he had $40 in the bank. Write and graph the equation that would represent howmuch money Terry has in the bank (y) after x hours of work. Identify the X- and the y-intercepts. Do they make sense in this context.

Answer 1

Equation: y = 14x + 40

x-intercept: x = -2.857

y-intercept: y = 40

Step-by-step explanation:

After x hours of works, Terry will have 14 times x in their bank account. Because he will have $14 for each hour worked.

Additionally, he already has $40 in the bank, so the equation that would represent how much money Terry has in the bank is:

y = 14x + 40

Then, the x-intercept is the value of x when y = 0, so we need to solve the following equation:

0 = 14x + 40

0 - 40 = 14x + 40 - 40

-40 = 14x

-40/14 = 14x/14

-2.857 = x

In the same way, the y-intercept is the value of y when x = 0, so replacing and solving for y, we get:

y = 14x + 40

y = 14(0) + 40

y = 0 + 40

y = 40

The x-intercept represents the moment when Terry has $0 in his account. Since it is -2.857, it doesn't have sense in this context.

The y-intercept represents the money in the bank when he has 0 hours of work. It is equal to $40, so it makes sense in this context.