Question

The given graph shows the relationship between the cost of shirts $\left(y\right)$ vs. the number of shirts $\left(x\right)$.


Which of the following functions shows that the cost of each shirt is the same as that is shown on the graph.

• A. $y=0.5x$
• B. $y=12x$
• C. $y=0.4x$
• D. $y=10x$

Answer 1

The correct option is D $y=10x$

The relationship can be written in the form of the table as shown below:
$\begin{array}{ccccccc}x& 1& 2& 3& 4& 5& 6\\ y& 10& 20& 30& 40& 50& 60\\ \frac{y}{x}& \frac{10}{1}=10& \frac{20}{2}=10& \frac{30}{3}=10& \frac{40}{4}=10& \frac{50}{5}=10& \frac{60}{6}=10\end{array}$
As the line passes through the origin, the equation of the line is of the form $y=mx,$
where $m$ is the constant of proportionality or slope.
Constant of proportionality, $m=\frac{y}{x}=10$
Cost of each shirt $=$ Constant of proportionality
$=\$10$
The function that shows the cost of each shirt as $\$10$ is given by
$\frac{y}{x}=10$
$\Rightarrow y=10x$.
$\to$ Option A is correct.