Question

Part 1: Create an equation of a line in point-slope form. Be sure to identify all parts of the equation before writing the equation.
Part 2: Using the equation of the line you wrote in part 1, write an equation of a line that is perpendicular to this line.

Answer 1

Covers the 'point-slope' form of linear equations, including how to find a line ... For this one, they give you a point (x1, y1) and a slope m, and have you plug it into this ... You can use the Mat way widget below to practice finding a line equation .... Find the equation of the line that passes through the points (–2, 4) and (1, 2)

Answer 2

Answer with explanation:

Part--1:

We know that a equation in point-slope form is represented by:

               $y-y_1=m(x-x_1)$

where m is the slope of the line and $(x_,y_1)$ is a point through which the line passes.  

  Consider a equation in a point-slope form as:

           $y-5=2(x-1)$

This means that the slope of the line is: 5

and the line  passes through the point (1,5).

Part--2:

Now as we know that if a line has a slope as m then the perpendicular line has a slope: -1/m

Since,

$m\times \text{Slope\ of\ second\ line}=-1\\\\i.e.\\\\\text{Slope\ of\ second\ line}=\dfrac{-1}{m}$

Let this perpendicular line passes through (2,6)

Hence, the equation of a line in point slope form is given by:

             $y-6=\dfrac{-1}{2}(x-2)$