Question

A scatter plot is made to model the amount of money left to pay on a credit card. The data used for the scatter plot are shown in the table:
Number of Months 3 5 1 2 0 4
Money Owed $1,400 $1,000 $1,800 $1,600 $2,000 $1,200


What does the y-intercept of the model represent?
The amount of the balance that has been paid that month
The monthly payments
The number of months it takes to pay off the credit card
The original balance on the credit card

Answer 1

Option d: The original balance on the credit card.

Explanation:

To determine the y-intercept, let us use the formula,

$y=mx+b$ where m is the slope and b is the y-intercept.

Also, $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Let us choose the coordinates $(3,1400)$ and $(5,1000)$

Substituting, we get,

$m=\frac{1000-1400}{5-3} =\frac{-400}{2} =-200$

Thus, the formula becomes

$y=-200x+b$

Now, to determine the value of b, let us substitute $(1,1800)$ in the formula,

we get,

$\begin{aligned}&1800=-200(1)+b\\&2000=b\end{aligned}$

Substituting the value of b in the formula, we have,

$y=-200 x+2000$

Thus, the y-intercept is $b=2000$

At y-intercept the value of x is 0. It means the y-intercept represents the amount of money left to pay on a credit card when the number of months is 0.

Thus, the y-intercept represents the original balance on the credit card.

Hence, Option d is the correct answer.