Question

question enola borrowed some money from her friend in order to help buy a new video game system. enola agreed to pay the friend back some amount every week until her loan was paid off. let l represent the amount enola owes her friend after t weeks. a graph of l is shown below. write an equation for l then state the x - intercept of the graph and determine its interpretation in the context of the problem. note: the line drawn is dotted because the domain of the function is limited to the integers. answer attempt 1 out of 2 l = the x - intercept of the function is which represents.

Explanation:

Step1: Find the slope

The line passes through $(0,105)$ and $(5, 5)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5 - 105}{5-0}=\frac{- 100}{5}=-20$.

Step2: Find the y - intercept

The line intersects the $y$-axis at $(0,105)$, so the $y$-intercept $b = 105$.

Step3: Write the linear - equation

Using the slope - intercept form $y=mx + b$, we have $L=-20t+105$.

Step4: Find the x - intercept

Set $L = 0$. Then $0=-20t + 105$. Solving for $t$ gives $20t=105$, so $t=\frac{105}{20}=5.25$. In the context of the problem, it represents the number of weeks it takes for Enola to pay off the entire loan (the amount owed $L$ becomes $0$).

Answer:

$L=-20t + 105$; The $x$-intercept of the function is $5.25$, which represents the number of weeks it will take for Enola to pay off the loan completely.