If y varies directly as x, then they have a proportional relationship that can be written as:
[tex]y=k\cdot x[/tex]
where k is a constant.
We know that, when x = 8, y = 120.
We can find the value of k, but as we only need to find the value of y when x = 13, we wil use a property of proportional relationships:
[tex]k=\frac{y_1}{x_1}=\frac{y_2}{x_2}[/tex]
This property tells us that the ratio y/x is constant for all pairs (x,y). Then, we can write:
[tex]\begin{gathered} (x_1,y_1)=(8,120) \\ (x_2,y_2)=(13,y) \end{gathered}[/tex]
Then, we can write the ratios as:
[tex]\begin{gathered} \frac{y_1}{x_1}=\frac{y_2}{x_2} \\ \frac{y}{13}=\frac{120}{8} \\ y=\frac{120}{8}\cdot13 \\ y=15\cdot13 \\ y=195 \end{gathered}[/tex]
NOTE: that we inplicitly calculated the value of k, that is k = 15. Then we know that the relation is y = 15x.
Answer: y = 195 when x = 13.
