Chapter 4, Problem 29SGR

To determine

To Calculate:

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

Answer to Problem 29SGR

The equation of line passing through (-2,1) and having slope -3 in point-slope form is :

  $y-1=-3(x+2)$

Explanation of Solution

Given Information:

Point through which the line passes is (-2,1) and slope of line is -3.

Formula Used:

Point-slope is a specific form of linear equations in two variables:

  $\begin{array}{l}y-y_1=m(x-x_1)\\ where\\ m=slope\\ (x_1,y_1)is\_po\mathrm{int}\_through\_which\_line\_passes\end{array}$

Calculation:

Given

  $\begin{array}{l}m=-3\\ (x_1,y_1)=(-2,1)\end{array}$

Substituting these values in the point-slope form :

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-1=-3(x-(-2))\mathrm{.................}[m=-3,(x_1,y_1)=(-2,1)]\\ \Rightarrow y-1=-3(x+2)\end{array}$

So,the equation of line passing through (-2,1) and having slope -3 in point-slope form is :

  $y-1=-3(x+2)$