Question

you will be given 3 attempts for this test. a zero will be entered if you do not take the test either by midnight or the next day. the zero will affect your grade. you can always take the test at a later time and the zero will be replaced by the grade you receive on the test. no points will be taken off for late submissions. all assignments are due at the end of the semester which is january 16th. $40 plus $20 for each day of the rental. the graph shows points representing the total cost of the rental. which linear equation, in slope - intercept form, models the total cost of the rental over time?\\(\boldsymbol{y = 50x + 25}\\)\\(\boldsymbol{y = 25x}\\)\\(\boldsymbol{y = 75x}\\)\\(\boldsymbol{y = x + 50}\\)\\(\boldsymbol{y = 20x + 40}\\)\\(\boldsymbol{\text{total cost}}\\)\\(\boldsymbol{(0,40)}\\)\\(\boldsymbol{(2,80)}\\)\\(\boldsymbol{(3,100)}\\)

Explanation:

Step1: Identify slope-intercept form

Slope-intercept form is $y = mx + b$, where $m$ is the daily cost (slope) and $b$ is the initial cost (y-intercept).

Step2: Find y-intercept ($b$)

From the graph, when $x=0$, $y=40$. So $b=40$.

Step3: Calculate slope ($m$)

Use points $(0,40)$ and $(2,80)$:
$m = \frac{80 - 40}{2 - 0} = \frac{40}{2} = 20$

Step4: Build the equation

Substitute $m=20$ and $b=40$ into $y=mx+b$.
$y = 20x + 40$

Answer:

$y = 20x + 40$