Question

The graph given below represents the proportional relationship between quantity $x$ and quantity $y$. Which of the following statement(s) is/are correct?

Answer 1

$\text{Detailed step-by-step solution:}$
Let’s consider two points $(0,0)$ and $(2,7)$ on the graph:
Constant of proportionality $=\frac{y}{x}$ (since the graph shows a proportional relationship between the quantities $x$ and $y)$
$=\frac{7}{2}x$
$=3.5$
$\frac{y}{x}=3.5$
$\Rightarrow y=3.5x$

$\text{The equation of the graph: y = 3.5x}$
Slope $=\frac{\text{Change in y}}{\text{Change in x}}$
$=\frac{7-0}{2-0}$
$=3.5$
Unit rate = Slope $=3.5$
Since unit change in x results in a change of $3.5$ units in $y$, a change of $4$ units in $x$ will result in a change of $\text{3.5 × 4 = 14}$ units in $y$.
All the statements are correct.
➡Option D is correct.