Option d: The original balance on the credit card.
Explanation:
To determine the y-intercept, let us use the formula,
[tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.
Also, [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let us choose the coordinates [tex](3,1400)[/tex] and [tex](5,1000)[/tex]
Substituting, we get,
[tex]m=\frac{1000-1400}{5-3} =\frac{-400}{2} =-200[/tex]
Thus, the formula becomes
[tex]y=-200x+b[/tex]
Now, to determine the value of b, let us substitute [tex](1,1800)[/tex] in the formula,
we get,
[tex]\begin{aligned}&1800=-200(1)+b\\&2000=b\end{aligned}[/tex]
Substituting the value of b in the formula, we have,
[tex]y=-200 x+2000[/tex]
Thus, the y-intercept is [tex]b=2000[/tex]
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.
