Question

Which of the following graphs represents a proportional relationship between y and x, where the unit rate of change of y with respect to x is 2.5?

Answer 1

$\text{Detailed step-by-step solution:}$
$\text{Checking for proportionality:}$
Since each graph is a straight line passing through the origin, all the graphs represent a proportional relationship between $x$ and $y$.

$\text{Calculating unit rate for each graph:}$
$A.$ Let’s take two points $(0,0)$ and $(2,6)$ on the graph:
$\text{Unit rate}=\frac{\text{Change in y}}{\text{Change in x}}$
$=\frac{6-0}{2-0}$
$\text{= 3}$

$B.$Let’s take two points $(0,0)$ and $(2,4)$ on the graph:
$\text{Unit rate}=\frac{\text{Change in y}}{\text{Change in x}}$
$=\frac{4-0}{2-0}$
$\text{= 2}$

$C.$Let’s take two points $(0,0)$ and $(2,5)$ on the graph:
$\text{Unit rate}=\frac{\text{Change in y}}{\text{Change in x}}$
$=\frac{5-0}{2-0}$
$\text{= 2.5}$

$D.$Let’s take two points $(0,0)$ and $(2,3)$ on the graph:
$\text{Unit rate}=\frac{\text{Change in y}}{\text{Change in x}}$
$=\frac{3-0}{2-0}$
$\text{= 1.5}$
The graph which represents a proportional relationship between $y$ and $x$, where the unit rate of change of $y$ with respect to $x$ is $2.5$. It is given in option C.
➡Option C is correct.