Answer:
The constant of proportionality is [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
The constant of proportionality is the ratio between two directly proportional quantities
- If x and y are in directly proportion, then [tex]\frac{y}{x}=k[/tex] , where k is the constant of proportionality.
- The direct proportion can be represented by a line whose equation is y = kx, where k is the slope of the line.
To find the constant of proportionality from the given graph choose a point on the line and substitute x and y in the equation of the proportionality by the coordinates of the point.
∵ Point (4, 18) lies on the line
∴ x = 4, y = 18
∵ The equation is y = kx
→ Substitute x by 4 and y by 18
∴ 18 = k(4)
∴ 18 = 4k
→ Divide both sides by 4 to find k
∴ [tex]\frac{18}{4}=\frac{4k}{4}[/tex]
∴ [tex]\frac{18}{4}=k[/tex]
→ Simplify the fraction by dividing up and down by 2
∴ [tex]\frac{9}{2}=k[/tex]
∴ The constant of proportionality is [tex]\frac{9}{2}[/tex]
