The percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer is given by
[tex]y=-0.2x+1[/tex]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
[tex]\begin{gathered} y=-0.2x+1 \\ 0=-0.2x+1 \\ 0.2x=1 \\ x=\frac{1}{0.2} \\ x=5 \end{gathered}[/tex]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
[tex]\begin{gathered} y=-0.2x+1 \\ y=-0.2(0)+1 \\ y=1 \end{gathered}[/tex]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)
[tex]\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=\frac{0.25}{0.2} \\ x=1.25\: \text{hours} \end{gathered}[/tex]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)
[tex]\begin{gathered} y=-0.2x+1 \\ y=-0.2(3)+1 \\ y=-0.6+1 \\ y=0.4 \end{gathered}[/tex]Therefore, the remaining battery power is 40% after 3 hours.
