Question

Write an equation in slope-intercept form for the line that satisfies each set of conditions.

Passes through $\left(\mathbf{6},\mathbf{4}\right)$ and $\left(\mathbf{8},-\mathbf{4}\right)$

Short answer

The equation of the required straight line in slope-intercept form is $y=-4x+28$.

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 given that the line passes through $\left(6,4\right)$and $\left(8,-4\right)$.

Then, $\left(h,k\right)=\left(6,4\right)$and $\left(a,b\right)=\left(8,-4\right)$.

– Write the equation

Put $\left(h,k\right)=\left(6,4\right)$and $\left(a,b\right)=\left(8,-4\right)$in $\frac{y-k}{x-h}=\frac{b-k}{a-h}$to get,

$\frac{y-4}{x-6}=\frac{-4-4}{8-6}$

$\frac{y-4}{x-6}=\frac{-8}{2}$ (Simplify)

$\frac{y-4}{x-6}=-4$ (Simplify)

$\frac{y-4}{x-6}\left(x-6\right)=-4\left(x-6\right)$ (Multiply both sides by $x-6$)

$y-4=-4\left(x-6\right)$ (Simplify)

$y-4=-4x+24$ (Distributive property)

$y-4+4=-4x+24+4$ (Add 4 to both sides)

$y=-4x+28$ (Simplify)

So, the required equation of the straight line in slope-intercept form is $y=-4x+28$.