Question

Write an equation in slope-intercept form of the line that passes through $\left(6,-1\right)$ and $\left(3,-7\right)$.

Answer 1

Find the slope-intercept form of an equation of a line.

It is given that the line passes through the points $\left(6,-1\right)$ and $\left(3,-7\right)$.

It is known that the slope of a line passes through two points $\left(x_1,y_1\right)$and $\left(x_2,y_2\right)$ is given by :

$m=\frac{y_2-y_1}{x_2-x_1}$

Substitute the given points in the above formula:

$$\begin{gathered} m=\frac{-7+1}{3-6} \\ \Rightarrow m=\frac{-6}{-3} \\ \Rightarrow m=2 \end{gathered}$$

The point-slope form of a line is $y-y_1=m\left(x-x_1\right)$ then the point-slope form of the line is $y+1=2\left(x-6\right)$.

Simplify this equation to get the slope-intercept form:

$\begin{array}{rcl}y+1& =& 2x-12\\ & \Rightarrow & y=2x-12-1\\ & \Rightarrow & y=2x-13\end{array}$

This is the slope-intercept form where $-13$ is the $y-$intercept.

Therefore, the required slope-intercept form of the line is $\mathit{y}\mathbf{=}\mathbf{2}\mathit{x}\mathbf{-}\mathbf{13}$.