Answers: Part (a). The equation is y = -0.2x+1 Part (b). The slope indicates that the power decreases by 20% per hour. The x intercept indicates that the battery lasts 5 hours. The y intercept indicates that the battery is at 100% when you turn on the laptop.Part (c). The battery is at 75% after 1.25 hours
For part (a), you don't need to type in the "y=" portion as that is already done for you. For any answer choice involving a percentage, type in the number only. This is because the percent sign is already taken care of.
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Explanation:
Part (a)
Note how each time x goes up by 1, y drops by 0.2
We can see that
slope = rise/run
slope = (change in y)/(change in x)
slope = (-0.2)/(1)
slope = -0.2
This tells us that the battery life goes down by 20 percentage points for each hour. Note: This is not the same as saying it drops by 20% each time, as this is a subtle difference; however, I can see what your teacher is trying to say for part (b).
The y intercept is b = 1 since this is the location where the graph crosses the y axis.
The slope m = -0.2 and y intercept b = 1 leads y = mx+b to turn into y = -0.2x+1 which is the final answer for part (a).
As a way to check, plug in x = 0 and you should get y = 1. Plug in x = 1 and you should get y = 0.8, and so on. The (x,y) values should match what the graph shows.
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Part (b)
As mentioned previously, the slope tells us how much the battery is changing. It's the rate of change. Specifically in this case, the battery is losing 20 percentage points for each hour. Your teacher should have used this careful phrasing, rather than say "the battery life goes down by 20% for each hour" but I can see what they're going for. So 20 is the answer for the first box of part (b)
The x intercept is where the graph crosses the x axis, which is x = 5 in this case. The x intercept always happens when y = 0. When y = 0, the battery is completely dead at 0%. Therefore, we can get 5 hours of battery life. The value 5 goes in the second box of part (b).
On the other end of the spectrum, the battery is 100% full when x = 0, which is at the start of everything. This is due to the y intercept b = 1.0 which represents 100%. In other words, the person starts off with a 100% charge, and they use their laptop for 5 hours, at which point the battery is at 0%. The value 100 goes in the third box for part (b)
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Part (c)
We are asked to find the value of x when y = 0.75
y = -0.2x+1
0.75 = -0.2x+1
0.75-1 = -0.2x
-0.25 = -0.2x
-0.2x = -0.25
x = -0.25/(-0.2)
x = 1.25
After 1.25 hours the battery is at 75%
