Question

tyler borrowed $900 from his friend to purchase a new video game console. he repays $125 each month. write an equation to represent the relationship between the amount tyler still owes and the number of months he has been repaying. then, describe the graph that would represent this relationship.

Explanation:

Step1: Define variables

Let $m$ be the number of months and $A$ be the amount Tyler still owes.

Step2: Write the equation

The initial amount borrowed is $900$ and he repays $125$ per month. So the equation is $A = 900- 125m$.

Step3: Describe the graph

The graph is a linear - function. The $y$ - intercept is $(0,900)$ (the amount owed at the start, when $m = 0$). The slope is $- 125$, which means the amount owed decreases by $125$ each month. As $m$ increases, $A$ decreases. The $x$ - intercept can be found by setting $A = 0$:
\[

$$\begin{align*} 0&=900 - 125m\\ 125m&=900\\ m&=\frac{900}{125}=\frac{36}{5} = 7.2 \end{align*}$$

\]
The graph is a straight - line that starts at the point $(0,900)$ and has a negative slope of $-125$, crossing the $x$ - axis at $m = 7.2$.

Answer:

The equation is $A = 900-125m$. The graph is a linear function with a $y$ - intercept of $(0,900)$ and a slope of $-125$, crossing the $x$ - axis at $m = 7.2$.