Question

willow alternates two figures, a square and a circle, in a repeating pattern on a wall. the table shows the number of feet the figures cover compared to the number of figures she uses. she plans to cover 36.5 feet of wall. how many figures will she stencil? step 1: make an estimate. the number of figures should be about 219. step 2: find the constant of proportionality, k. k = \frac{square}{square}=square the constant of proportionality is square figures per foot. table length covered (ft) x number of figures y 3 18 6 36 9 54 36.5

Explanation:

Step1: Calculate the constant of proportionality

The formula for the constant of proportionality $k$ in a proportional relationship $y = kx$ is $k=\frac{y}{x}$. Taking the first - row values from the table where $x = 3$ and $y = 18$, we have $k=\frac{18}{3}=6$.

Step2: Confirm the constant of proportionality

We can check with other rows. For the second row, $x = 6$ and $y = 36$, and $\frac{y}{x}=\frac{36}{6}=6$. For the third row, $x = 9$ and $y = 54$, and $\frac{y}{x}=\frac{54}{9}=6$.

Answer:

$k=\frac{18}{3}=6$; 6