Question

Write an equation in point-slope form for the line that passes through the given point with the slope provided.

$\left(-2,1\right)$, slope $-3$

Short answer

The equation of the line in point-slope form is $\mathit{y}\mathbf{-}\mathbf{1}\mathbf{=}\mathbf{-}\mathbf{3}\left(x+2\right)$.

Step-by-step solution

Step 1. The equation in the point-slope form:

The equation of the line passing through the point $\left(x_1,y_1\right)$and having slope $m$, in point-slope form is given by,

$y-y_1=m\left(x-x_1\right)\mathrm{.........}\left(1\right)$

Step 2. Write an equation for the line passing through the point (−2,1) having slope −3. 

Substitute $x_1=-2,y_1=1$and $m=-3$in (1),

$$\begin{gathered} y-1=-3\left(x-\left(-2\right)\right) \\ y-1=-3\left(x+2\right) \end{gathered}$$

Therefore, the equation of the line in point-slope form is $y-1=-3\left(x+2\right)$.