Question

question tamika borrowed some money from her friend in order to help buy a new video game system. tamika agreed to pay the friend back some amount every week until her loan was paid off. let l represent the amount tamika 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 $(0,100)$ and $(20,0)$. Slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 100}{20-0}=-5$.

Step2: Find the y - intercept

The line intersects the $y$-axis at $(0,100)$, so $b = 100$.

Step3: Write the equation

Using the slope - intercept form $y=mx + b$, we have $L=-5t + 100$.

Step4: Find the x - intercept

Set $L = 0$, then $0=-5t + 100$, solving for $t$ gives $t = 20$. In the context, it's the number of weeks to pay off the loan.

Answer:

$L=- 5t + 100$; The $x$-intercept of the function is $20$, which represents the number of weeks it will take for Tamika to pay off the loan completely.