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The given information is an illustration of a linear function; such that:
6. The equation of the function is: [tex]y = 16x[/tex]
7. It takes 16 hours to paint an area of 256 square feet
Given that:
[tex]\left[\begin{array}{cccccc}Time&4&9&25\\Amount&64&144&400\end{array}\right][/tex]
Let:
[tex]x \to[/tex] Time
[tex]y \to[/tex] Area of a wall
6. The equation of the table
First, calculate the slope (m) of the table:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{144-64}{9-4}[/tex]
[tex]m = \frac{80}{5}[/tex]
[tex]m = 16[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = 16(x - 4) + 64[/tex]
[tex]y = 16x - 64 + 64[/tex]
[tex]y = 16x[/tex]
7. Time spent for an area of 256 square feet
This implies that:
[tex]y = 256[/tex]
So, we have:
[tex]y = 16x[/tex]
[tex]256 = 16x[/tex]
Divide both sides by 16
[tex]16 = x[/tex]
[tex]x = 16[/tex]
Hence, Sharon will spend 16 hours to paint 256 square feet
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