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# The table shows the percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer.$\begin{matrix} \text{Hours, x} & \text{0} & \text{2} & \text{4}\\ \text{Power Remaining, y} & \text{1.0} & \text{0.6} & \text{0.2}\\ \end{matrix}$a. Write and graph a linear function that relates y to x. b. Interpret the slope, the x-intercept, and the y-intercept. c. After how many hours is the battery power at 75%?

Solution

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$\textbf{a. }$The linear function has the form

$y=mx+c$

and Slope of the function is given by

$m=\frac{y_2-y_1}{x_2-x_1}$

Given:

$(x_1,y_1)=(2,0.6)$

$(x_2,y_2)=(4,0.2)$

So,

$m=\frac{0.2-0.6}{4-2}=\frac{-0.4}{2}=-0.2$

The line of the function passes through $(0,1)$. So, $c=1$. Function for $y$ is

$y=-0.2x+1$

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