Question

11. Write an equation in slope-intercept form for the graph at the right.

Short answer

The equation of the required straight line in slope-intercept form is $y=\frac{5}{4}x+7$.

Step-by-step solution

– State the concept

The slope intercept form of a straight-line equation is $y=mx+c$ where $m$ is the slope and $c$ is the y-intercept.

The equation of a straight-line passing through the points $\left(h,k\right)$ and $\left(a,b\right)$ is given as $\frac{y-k}{x-h}=\frac{b-k}{a-h}$.

– List the given data

It is clear, from the graph, that the line passes through $\left(-4,2\right)$ and $\left(0,7\right)$.

Then, $\left(h,k\right)=\left(-4,2\right)$ and $\left(a,b\right)=\left(0,7\right)$.

– Write the equation

Put $\left(h,k\right)=\left(-4,2\right)$ and $\left(a,b\right)=\left(0,7\right)$ in $\frac{y-k}{x-h}=\frac{b-k}{a-h}$ to get,

$\frac{y-2}{x-\left(-4\right)}=\frac{7-2}{0-\left(-4\right)}$

$\frac{y-2}{x+4}=\frac{5}{4}$ (Simplify)

$\frac{y-2}{x+4}\left(x+4\right)=\frac{5}{4}\left(x+4\right)$ (Multiply both sides by $x+4$)

$y-2=\frac{5}{4}\left(x+4\right)$ (Simplify)

$y-2=\frac{5}{4}x+5$ (Distributive property)

$y-2+2=\frac{5}{4}x+5+2$ (Add 2 to both sides)

$y=\frac{5}{4}x+7$ (Simplify)

So, the required equation of the straight line in slope-intercept form is $y=\frac{5}{4}x+7$.