Question

In order in order to build a shed you need to build 6 inches of height for a base that is 26 inches long. What is the height of a shed that is 156 inches long?Part A: What is the equation that represents this relationship y=blankPart B: A shed that is 156 inches long is blank inches high

Answer 1

A.

Let y represent the length of the shed and x the height;

Then we can represent it with the equation;

$\begin{gathered} y\propto x \\ y=kx \end{gathered}$

To get k, at y=26, x =6;

Substituting the values to the equation above;

$\begin{gathered} y=kx \\ 26=k(6) \\ k=\frac{26}{6} \\ k=\frac{13}{3} \end{gathered}$

Therefore, the equation will be;

$y=\frac{13}{3}x$

B.

For a shed that is 156 inches long, the height will be;

y=156

$\begin{gathered} y=156=\frac{13}{3}x \\ x=156\times\frac{3}{13} \\ x=36\text{ inches} \end{gathered}$

Therefore, the shed that long is 36 inches high.

$36\text{ inches}$