Tara creates a budget for her weekly expenses. The graph shows how much money is
in the account at different times. Find the slope of the line. Then tell what rate the slope
represents.

a.

The slope is . The slope means that the amount of money in the
account is decreasing at a rate of $50 every week.

b.

The slope is 50. The slope means that the
amount of money in the account is increasing at a rate of $50 every week.

c.

The slope is . The slope means that the amount of money in the account is decreasing at a rate of $0.02
every week.

d.

The slope is . The slope means that the amount of money in the
account is decreasing at a rate of $50 every 2 weeks.

Mr. Jackson and Mrs. Gutierrez have monthly payments to pay off their car
loans. The table and graph show their loan information. Compare the loans by finding and
interpreting slopes and y-intercepts.

Mrs. Gutierrez’ Loan

Mr. Jackson’s Loan

Months

0

2

4

6

Loan Balance ($)

6500

5900

5300

4700

a.

For Mrs. Gutierrez’ loan, the slope is –$350 and the y-intercept
is $12,000. For Mr. Jackson’s loan, the slope is –$300 and the y-intercept is
$6,500. The slope is the beginning loan balance. The y-intercept is the rate of change, or
the monthly payment. Mrs. Gutierrez had the greater initial balance than Mr. Jackson. Mrs.
Gutierrez is also paying more per month than Mr. Jackson.

b.

For Mr.
Jackson’s loan, the slope is –$350 and the y-intercept is $12,000. For Mrs.
Gutierrez’ loan, the slope is –$300 and the y-intercept is $6,500. The slope is
the rate of change, or the monthly payment. The y-intercept is the beginning loan
balance. Mr. Jackson had the greater initial balance than Mrs. Gutierrez. Mr. Jackson is also
paying more per month than Mrs. Gutierrez.

c.

For Mrs. Gutierrez’ loan, the slope is
–$700 and the y-intercept is $12,000. For Mr. Jackson’s loan, the slope is
–$600 and the y-intercept is $6,500. The slope is the rate of change, or the monthly
payment. The y-intercept is the beginning loan balance. Mrs. Gutierrez had the greater
initial balance than Mr. Jackson. Mrs. Gutierrez is also paying more per month than Mr.
Jackson.

d.

For Mrs. Gutierrez’ loan, the slope is –$350 and the y-intercept
is $12,000. For Mr. Jackson’s loan, the slope is –$300 and the y-intercept is
$6,500. The slope is the rate of change, or the monthly payment. The y-intercept is the
beginning loan balance. Mrs. Gutierrez had the greater initial balance than Mr. Jackson. Mrs.
Gutierrez is also paying more per month than Mr. Jackson.

Essay

1.

A student borrowed money for medical school costs. The student agreed to work in
a county with a depressed economy, so the loan is interest free, requiring only regular monthly
payments after graduation. After 41 monthly payments, the loan balance was $36,919. After 72 monthly
payments, the loan balance was $23,248.

What is the slope of the
line passing through the points representing the loan balance? Show the calculation and explain what
the slope represents.