Question

mr. green uses a linear function to estimate how installing solar panels on the roof of his house will reduce his electric bill.

• mr. green does not have any solar panels yet, and his electric bill is $133 per month on average.
• for each 100 square feet of solar panels he installs, mr. greens monthly electric bill will decrease by $13.50.

how many square feet of solar panels must mr. green install to reduce his monthly electric bill to $25?
□ square feet
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Explanation:

Step1: Define the linear function

Let \( x \) be the number of 100 - square - feet units of solar panels installed, and \( y \) be the monthly electric bill. The initial bill (when \( x = 0 \)) is \( y_0=133 \), and the slope \( m=- 13.50 \) (since the bill decreases as solar panels are installed). The linear function is \( y = 133-13.5x \). We want to find \( x \) when \( y = 25 \).

Step2: Solve for \( x \)

Set \( y = 25 \) in the equation \( 25=133 - 13.5x \).
First, subtract 133 from both sides: \( 25-133=-13.5x \).
\( - 108=-13.5x \).
Then, divide both sides by - 13.5: \( x=\frac{- 108}{-13.5}=8 \).

Step3: Find the number of square feet

Since \( x \) is the number of 100 - square - feet units, the number of square feet \( S=100x \). Substitute \( x = 8 \) into the formula, we get \( S = 100\times8 = 800 \).

Answer:

800