Select the correct answer:

William recorded data to determine the relationship between the time usage, [tex]x[/tex], and the percentage of charge left on his mobile phone, [tex]y[/tex]. He graphed the data and drew the line of best fit. The equation of the line of best fit is [tex]y = -10x + 100[/tex]. About how many hours will it take for the phone to lose its charge completely?

A. about 5 hours
B. about 10 hours
C. about 20 hours
D. about 22 hours
E. about 24 hours



Answer :

To determine when William's phone will lose its charge completely, we can use the given equation of the line of best fit, which is [tex]\( y = -10x + 100 \)[/tex].

Here, [tex]\( y \)[/tex] represents the percentage of charge left, and [tex]\( x \)[/tex] represents the time in hours. We need to find out when the phone's charge percentage [tex]\( y \)[/tex] becomes [tex]\( 0 \)[/tex].

Given the equation:
[tex]\[ y = -10x + 100 \][/tex]

Set [tex]\( y \)[/tex] to [tex]\( 0 \)[/tex] and solve for [tex]\( x \)[/tex]:
[tex]\[ 0 = -10x + 100 \][/tex]

To isolate [tex]\( x \)[/tex], we start by moving [tex]\( -10x \)[/tex] to the other side of the equation:
[tex]\[ 10x = 100 \][/tex]

Next, divide both sides of the equation by 10:
[tex]\[ x = \frac{100}{10} \][/tex]

Thus, solving the equation gives:
[tex]\[ x = 10 \][/tex]

So, it will take about 10 hours for the phone to lose its charge completely.

The correct answer is:
B. about 10 hours