Question

The given graph shows a proportional relationship between the number of tennis balls sold $\left(n\right)$ and their cost $\left(c\right)$. Which of the following statements about the graph are true?

I. The equation of the graph is $n=0.2c.$
II. The equation of the graph is $c=0.2n.$
III. Each tennis ball costs $\$5.$
IV. Each tennis ball costs $\$\mathrm{0.2.}$

• A. Only statement IV.
• B. Only statement I.
• C. Both statement I and statement III.
• D. Both statement II and statement IV.

Answer 1

The correct option is C Both statement I and statement III.

Equation of the graph:
The cost of each tennis ball is represented by $c.$
The number of tennis balls sold is represented by $n.$
Slope $=\frac{y_2-y_1}{x_2-x_1}=\frac{8-4}{40-20}=\frac{4}{20}=0.2$
As the line passes through the origin, its y-intercept is $0.$
The slope-intercept form of a line is $y=mx+b,$ where $m$ is the slope and $b$ is the y-intercept of the line.
Therefore, the equation of the graph will be $n=0.2c.......\left(1\right)$
Hence, statement I is correct.

Cost of one tennis ball:
When $n=1,$ equation (1) becomes:
$1=0.2\times c$
$\Rightarrow c=\frac{1}{0.2}$
$\Rightarrow c=\frac{10}{2}$
$\Rightarrow c=5$
The cost of each tennis ball is $\$5$.
Hence, statement III is correct.