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. reset step table length covered (ft) x number of figures y 3 18 6 36 9 54

Explanation:

Step1: Find the constant of proportionality

We can see from the table that the ratio of the number of figures $y$ to the length covered $x$ is constant. For example, when $x = 3$, $y=18$, and $\frac{y}{x}=\frac{18}{3} = 6$. When $x = 6$, $y = 36$, and $\frac{y}{x}=\frac{36}{6}=6$. When $x = 9$, $y = 54$, and $\frac{y}{x}=\frac{54}{9}=6$. So the constant of proportionality $k = 6$.

Step2: Calculate the number of figures

We know that the length to be covered is $x = 36.5$ feet. Using the equation $y=kx$ (where $k = 6$), we substitute $x$ into the equation: $y=6\times36.5=219$.

Answer:

219