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Chapter 1: Q. 67 (page 41)

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 2x+y=2

containing the point(-3,0)

Short Answer

Expert verified

The equation of the line isy=12x+32

Step by step solution

01

Step 1. Given information

The perpendicular line is 2x+y=2

The point is(-3,0)

02

Step 2. Finding the slope of line

Firstly, find the slope of a perpendicular line

2x+y=2

Solve for y

y=-2x+2

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=-1-2m=12

03

Step 3. Finding the equation of line

The slope of line is

m=12

The point is

(x1,y1)=(-3,0)

Apply point-slope formula

y-y1=m(x-x1)

Plug values

y-0=12(x+3)y=12x+32

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