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Chapter 1: Q 13. (page 51)

For the line 2x+3y=6, find a line parallel to it containing the point 1,-1.Also find a line perpendicular to it containing the point 0,3.

Short Answer

Expert verified

Line parallel to 2x+3y=6this line is 2x+3y=-1and the line perpendicular to this line isrole="math" localid="1646139517622" 2x+3y=-9.
.

Step by step solution

01

Step 1. Given information.

Consider the given line2x+3y=6and points1,-1and0,3.

02

Step 2. Compare the equation with the slope intercept form of the equation of line.

Equation of slope intercept form is y=mx+bwhere m is slope and bis yintercept.

2x+3y=63y=-2x+6y=-23x+2

For parallel lines m1=m2where m1=-23

Further simplify to findm2.

03

Step 3. To use point slope form of equation of line.

Point slope form of equation of line is y-y1=mx-x1.

Substitute the value of x1=1,y1-1and m=-23.

y+1=-23x-12x+3y=-1

Solving this equation in the form of y=mx+bwe get the value of m2=-23.

Thereforem1=m2so the lines are parallel.

04

Step 4. Formula and slope property used to show that both the lines are perpendicular.

Formula used to find the equation of line is y-y1=mx-x1and for two lines to be perpendicular m1m2=-1.

Substitute the value of x1=0,y1=3Therefore the equation of line is role="math" localid="1646139325397" 2x+3y=-9.So both the lines are perpendicular .

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