1 Answer

Konstantinos Gallis · Answer 1 · 2023-10-01T01:21:44+0000

The percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer is given by

Let us graph the above equation

a. What is the x-intercept? What does it represent?

The x-intercept is the point where the line intersects the x-axis.

From the graph, we can see that the x-intercept is (5, 0)

The x-intercept represents that it takes 5 hours for the battery power to go to 0%

You can manually find out the x-intercept by substituting y = 0 into the given equation

$\begin{gathered} y=-0.2x+1 \\ 0=-0.2x+1 \\ 0.2x=1 \\ x=(1)/(0.2) \\ x=5 \end{gathered}$

Therefore, the x-intercept is (5, 0)

b. What is the y-intercept? What does it represent?

The y-intercept is the point where the line intersects the y-axis.

From the graph, we can see that the y-intercept is (0, 1)

The y-intercept represents that the battery power is 1 (100%) when x = 0 hours.

You can manually find out the y-intercept by substituting x = 0 into the given equation

$\begin{gathered} y=-0.2x+1 \\ y=-0.2(0)+1 \\ y=1 \end{gathered}$

Therefore, the y-intercept is (0, 1)

c. After how many hours is the battery power at 75%

We need to substitute y = 0.75 (that means 75%) into the equation to find out x (number of hours)

$\begin{gathered} y=-0.2x+1 \\ 0.75=-0.2x+1 \\ 0.75+0.2x=1 \\ 0.2x=1-0.75 \\ 0.2x=0.25 \\ x=(0.25)/(0.2) \\ x=1.25\: \text{hours} \end{gathered}$

Therefore, after 1.25 hours, the battery power is at 75%

d. what is the percentage of battery power remaining at 3 hours?

We need to substitute x = 3 hours into the equation to find out y (remaining battery power)

$\begin{gathered} y=-0.2x+1 \\ y=-0.2(3)+1 \\ y=-0.6+1 \\ y=0.4 \end{gathered}$

Therefore, the remaining battery power is 40% after 3 hours.

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