Question

The given graph represents the fee Kevin charges for babysitting in dollars $\left(y\right)$ based on the number of hours $\left(x\right)$. What is the equation of the graph?

• A. $y=5.5x$
• B. $y=7.5x$
• C. $y=11x$
• D. $y=10x$

Answer 1

The correct option is B $y=7.5x$


The line is straight and passes through the origin and hence represents a proportional relationship. So, equation representing this must be of the form
$y=kx$, where k represents the slope of the line.
Consider points $(0,0)$ and $(4,30)$.

$\text{Slope}=\frac{\text{rise}}{\text{run}}$

$=\frac{\text{change in}y}{\text{change in}x}$

$=\frac{30-0}{4-0}$

$=\frac{30}{4}=\frac{15}{2}=7.5$

Equation of the graph is given by: $y=\text{slope}\times x$

$\Rightarrow y=7.5x$