Question

5. MaryAnne painted 600 square feet of wall space using 1 1/2gallons of paint. The number of

square feet she can paint, y, is proportional to the number of gallons used, x.
k=
Equation:

Answer 1

The equation that represents the relationship between the number of square feet painted (y) and the number of gallons of paint used (x) can be expressed as follows:

`\displaystyle\sf y = kx`,

where
`\displaystyle\sf k` represents the constant of proportionality.

In this specific scenario, MaryAnne painted 600 square feet of wall space using 1 1/2 gallons of paint. To find the value of
`\displaystyle\sf k`, we can substitute the given values into the equation:

`\displaystyle\sf 600 = k \cdot \left( (3)/(2) \right)`.

To solve for
`\displaystyle\sf k`, we can multiply both sides of the equation by
`\displaystyle\sf (2)/(3)`:

`\displaystyle\sf (2)/(3) \cdot 600 = k`,

`\displaystyle\sf k = 400`.

Therefore, the equation representing the relationship between the number of square feet painted (y) and the number of gallons of paint used (x) is:

`\displaystyle\sf y = 400x`.