Given:
The graph of a proportional relationship.
To find:
The constant of proportionality, the value of y when x is 24 and the value of x when y is 108.
Solution:
If y is directly proportional to x, then
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
Where, k is the constant of proportionality.
The graph of proportional relationship passes through the point (5,15).
Substituting x=5 and y=15 in (i), we get
[tex]15=k(5)[/tex]
[tex]\dfrac{15}{5}=k[/tex]
[tex]3=k[/tex]
Therefore, the constant of proportionality is 3.
Substituting k=3 in (i) to get the equation of the proportional relationship.
[tex]y=3x[/tex] ...(ii)
Substituting x=24 in (ii), we get
[tex]y=3(24)[/tex]
[tex]y=72[/tex]
Therefore, the value of y is 72 when x is 24.
Substituting y=108 in (ii), we get
[tex]108=3x[/tex]
[tex]\dfrac{108}{3}=y[/tex]
[tex]36=y[/tex]
Therefore, the value of x is 36 when y is 108.