B
1) Let's redo the steps Heather did when calculating this. Note that direct variation can be generally written as:
[tex]y=kx[/tex]
2) Heather was told that when y=8 then z=8 so let's find the constant of proportionality (k) plugging into the formula below into y and z the given values:
[tex]\begin{gathered} y^3=kz \\ (8)^3=k(8) \\ 512=8k \\ 8k=512 \\ \frac{8k}{8}=\frac{512}{8} \\ k=64 \end{gathered}[/tex]
Now we know the value of k, let's test that and then mark the right choice
[tex]\begin{gathered} y^3=k\cdot z \\ y³=64\cdot8 \\ y=\sqrt[3]{512} \\ y=8 \end{gathered}[/tex]
The first error then was:
b. She substituted incorrectly when calculating the constant of variation.
