Q. 66 - Precalculus Enhanced with Graphing Utilities

Question

Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer.

Perpendicular to the line $y=2x-3$; containing the point $(1,-2)$.

Step-by-Step Solution

Answer

The equation of the line is 

$y=-\frac{1}{2}x-\frac{3}{2}$

Step 1. Given information

The perpendicular line is $y=2x-3$

The point is $(1,-2)$.

Step 2. Finding the slope of line

Firstly, find the slope of a perpendicular line $y=2x-3$

Compare with slope-intercept formula

$y=mx+b$

So, slope is $2$

Since slope of perpendicular line is always negative of inverse of the other line slope.

So, slope is 

$m=-\frac{1}{2}$

Step 3. Finding the equation of line

The slope of line is

 $m=-\frac{1}{2}$

The point is 

$(x_1,y_1)=(1,-2)$

Apply point-slope formula

$y-y_1=m(x-x_1)$

Plug values

$y+2=-\frac{1}{2}(x-1)$

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