Question

liam rented a pedal - board for 5.5 hours and paid a total of $93.75. what is an equation in point - slope form that models the cost of renting a pedal board for x hours? how can liam use the equation to find the one - time service charge? if y is the total cost of the rental, then y - 93.75 = 12.5(x - 5.5) models the cost of renting a pedal board for x hours. (type an equation. type your answer in point - slope form. use integers or decimals for any numbers in the equation. do not include the $ symbol in your answer.) liam should rewrite the equation from the previous step so that y is isolated on one side. the on the other side is then the service fee.

Explanation:

Step1: Identify the slope - intercept form

The slope - intercept form is $y = mx + b$, where $m$ is the rate per hour and $b$ is the one - time service charge. Given that the rate per hour $m = 12.50$, and when $x = 5.5$ hours, $y=93.75$. The equation $y-93.75 = 12.5(x - 5.5)$ can be rewritten in slope - intercept form. First, expand the right side: $y-93.75=12.5x-12.5\times5.5$.

Step2: Calculate the right - hand side value

$12.5\times5.5 = 68.75$, so $y-93.75=12.5x - 68.75$.

Step3: Isolate $y$

Add 93.75 to both sides of the equation: $y=12.5x+(93.75 - 68.75)$.

Step4: Calculate the one - time service charge

$93.75−68.75 = 25$, so the equation is $y = 12.5x+25$.

Answer:

$y = 12.5x + 25$