Question

which equation models the graph shown? *
number of car payments
remaining owed
-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-400
400
800
1200
1600
2000
f(x)=20 + 2500x
f(x)=-125x + 2500
y=-2500x + 20
y=-500x + 20

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept

The line crosses the y - axis at $y = 2500$, so $b = 2500$.

Step3: Calculate the slope

The line passes through $(0,2500)$ and $(20,0)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 2500}{20-0}=\frac{-2500}{20}=- 125$.

Step4: Write the equation

Substitute $m=-125$ and $b = 2500$ into $y=mx + b$, we get $y=-125x + 2500$ or $f(x)=-125x + 2500$.

Answer:

$f(x)=-125x + 2500$