Question

student loan repayment
student loan amount
(in thousands of dollars)
time (in years)
the graph above shows a line of best fit for data collected on the amount of student loans in relation to the number of years it takes to pay them back. what is the equation of the line of best fit?
a. $y = -\frac{3}{4}x + 11,000$
b. $y = -750x + 11,000$
c. $y = -\frac{3}{4}x + 11$
d. $y = -750x + 11$

Explanation:

Step1: Identify y-intercept

The line crosses y-axis at (0,11). Since y is in thousands of dollars, y-intercept is 11.

Step2: Calculate slope

Take two points on the line: (0,11) and (12,1). Slope $m=\frac{1-11}{12-0}=-\frac{10}{12}=-\frac{5}{6}?$ No, wait—check (0,11) and (8,5): $m=\frac{5-11}{8-0}=-\frac{6}{8}=-\frac{3}{4}$.

Step3: Match equation

Slope $-\frac{3}{4}$, intercept 11. Equation: $y=-\frac{3}{4}x +11$.

Answer:

C. $y = -\frac{3}{4}x + 11$