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Use the following information to answer #6-7: Sharon is painting a wall. The table below shows the number of hours of painting and the amount of a wall painted in square feet.

Sagot :

MrRoyal

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

Read more about linear functions at:

https://brainly.com/question/20286983

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