The checking account is modeled as a linear function from the data given.
There is a constant decrease every month.
x represents the months
y represents the balance at the end of every month.
[tex]\begin{gathered} P\text{ icking 2 points to get the slope of the function,} \\ (0,800)\text{ and (1,717.5)} \\ \text{where} \\ x_1=0 \\ y_1=800 \\ x_2=1 \\ y_2=717.5 \\ \text{The slope m, is given by} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{717.5-800}{1-0} \\ m=\frac{-82.5}{1} \\ m=-82.5 \end{gathered}[/tex]
The slope represents a monthly decrease of $82.5
This shows it is a linear function.
And a linear function is of the form y = mx + C
[tex]\begin{gathered} y=-82.5x+C \\ P\text{ icking a point out to get C,} \\ (0,800) \\ x=0 \\ y=800 \\ y=-82.5x+C \\ 800=-82.5(0)+C \\ 800=0+C \\ C=800 \\ \\ \text{Hence, the equation is;} \\ y=-82.5x+800 \end{gathered}[/tex]
Therefore, the model that best illustrates the situation is y = -82.5x + 800
The correct answer is the third option.
