Question

A line passes through the point $\left(8,4\right)$ and has a slope of $-\frac{3}{4}$.

Write an equation in slope-intercept form for this line.

Answer 1

Form an equation of the line:

Given the line passes through $\left(8,4\right)$

So, $\left(x_1,y_1\right)$ is $\left(8,4\right)$

Also the slope of the line is $m$ is equal to $-\frac{3}{4}$

The formula for the equation of the line using slope-intercept form is $y-y_1=m\left(x-x_1\right)$

Substitute $x_1$ as $8$ , $y_1$ as $4$ and $m$ as $-\frac{3}{4}$

$$\begin{gathered} y-4=-\frac{3}{4}\left(x-8\right) \\ \Rightarrow 4\left(y-4\right)=-3\left(x-8\right)\left[\mathrm{Multiplying}4\mathrm{on}\mathrm{both}\mathrm{sides}\right] \\ \Rightarrow 4y-16=-3x+24\left[\mathrm{Solve}\mathrm{the}\mathrm{parentheses}\right] \\ \Rightarrow 3x+4y=16+24\left[\mathrm{Adding}3x+16\mathrm{on}\mathrm{both}\mathrm{sides}\right] \\ \therefore 3x+4y=40 \\ \Rightarrow y=\frac{-3x}{4}+10 \end{gathered}$$

Hence, the equation of the line is $3x+4y=40\Rightarrow y=\frac{-3x}{4}+10$.