As y varies directly as x, we have a linear relation for x and y that goes through the origin (the point (0, 0) belongs to the line).
Other point that belongs to the linear relation is (x=15; y=48).
We have the relation:
[tex]y=mx+b[/tex]b=0, as y varies directly as x.
Using the point (15, 48) we have:
[tex]\begin{gathered} 48=m\cdot15+0 \\ m=\frac{48}{15} \\ m=3.2 \end{gathered}[/tex]Then, the equation that relates y to x is:
[tex]y=3.2x[/tex]When y=16, this corresponds to an x value of:
[tex]\begin{gathered} y=16=3.2x \\ x=\frac{16}{3.2}=5 \end{gathered}[/tex]When y=16, x=5.
