Question

this question has two parts. first, answer part a. then, answer part b.
part a
loan ross borrows $5625 to buy a car. he pays back $125 each month. the equation $y = 5625 - 125x$ represents that amount ross owes $y$ after $x$ months.
a. find the $x$- and $y$-intercepts and interpret their meaning in the context of the situation.
the $x$-intercept is \boxed{}. this means that after \boxed{} months, ross will owe $\boxed{}$. the $y$-intercept is \boxed{}. this means that ross initially owed $\boxed{}$.
part b
b. graph the equation using the intercepts.
\bigcirc a) \

$$\begin{tikzpicture}scale=0.5 \\draw-> (0,0) -- (60,0) noderight {$x$}; \\draw-> (0,0) -- (0,6000) nodeabove {$y$}; \\drawthick, blue (0,5500) -- (20,0); \\foreach \\x in {0,10,20,30,40,50,60} \\draw (\\x,0) -- (\\x,-3) nodebelow {$\\x$}; \\foreach \\y in {0,500,1000,1500,2000,2500,3000,3500,4000,4500,5000,5500,6000} \\draw (0,\\y) -- (-3,\\y) nodeleft {$\\y$}; \ oderotate=90 at (-5, 3000) {amount owed}; \\end{tikzpicture}$$

Explanation:

Part A

Step1: Find x - intercept

The x - intercept is the value of \(x\) when \(y = 0\). We set \(y=0\) in the equation \(y = 5625-125x\).

$$
LATEXBLOCK0
$$

This means that after 45 months, Ross will owe \(\$0\) (since \(y = 0\) at \(x = 45\)).

Step2: Find y - intercept

The y - intercept is the value of \(y\) when \(x = 0\). We set \(x = 0\) in the equation \(y=5625 - 125x\).

$$ y=5625-125\times0=5625 $$

This means that Ross initially (when \(x = 0\), 0 months have passed) owed \(\$5625\).

To graph the equation \(y=5625 - 125x\) using the intercepts:

• The x - intercept is at the point \((45,0)\) (from Part A, when \(y = 0\), \(x = 45\)).
• The y - intercept is at the point \((0,5625)\) (from Part A, when \(x = 0\), \(y = 5625\)).

We plot these two points on a coordinate plane (with the x - axis representing the number of months and the y - axis representing the amount owed) and draw a straight line connecting them. Looking at the given options, the graph in option A (the one with the line connecting \((0,5625)\) and \((45,0)\) approximately, though the graph in the problem has a typo in the x - intercept marking, the correct x - intercept is 45) should be the correct graph as it uses the y - intercept (\(y = 5625\) when \(x = 0\)) and should use the x - intercept (\(x = 45\), \(y = 0\)) to draw the line.

Answer:

The x - intercept is \(45\). This means that after \(45\) months, Ross will owe \(\$0\). The y - intercept is \(5625\). This means that Ross initially owed \(\$5625\).

Part B