Question

The given graph shows a proportional relationship between the number of shirts $\left(x\right)$ Clarke buys and the price $\left(y\right)$ he pays to buy them.


What is the constant of proportionality?

• A. $2$
• B. $1$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

Identify the coordinates of any point on the line. Let’s consider the coordinates $(1,3).$

$\Rightarrow x=1\text{and}y=3$
Since this is a straight line passing through the origin, it represents a proportional relationship. We find the ratio between the two values x and y to find the constant of proportionality.
Ratio of the y-coordinate to the x-coordinate $=\frac{y}{x}=\frac{3}{1}=3$
Hence, the constant of proportionality is $3.$
If the price of $1$ shirt is $\$3,$ the price for $2$ shirts will be $2\times 3=\$6$ and so on.