Question

Consider the line y=7x-5.

Find the equation of the line that is perpendicular to this line and passes through the point (-3, – 3).
Find the equation of the line that is parallel to this line and passes through the point (-3, – 3).
Equation of perpendicular line: 0
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Equation of parallel line:

Answer 1

a)The equation of the Parallel line to the given line is

7x -y +18 =0

b) The equation of the Perpendicular line to the given line is

-x +7y +18 =0

Explanation:

Step(i):-

Given that equation of the line y = 7x -5

7x -y -5=0

The equation of the Parallel line to the given line is

7x -y +k=0

This line is passes through the point ( -3,-3)

7 ( -3) -(-3)+k=0

-21 +3+k=0

-18 +k=0

k =18

The equation of the Parallel line to the given line is

7x -y +18 =0

Step(ii):-

Given that equation of the line y = 7x -5

7x -y -5=0

The equation of the perpendicular line

b x -ay +k=0

The equation of the Perpendicular line to the given line is

-x +7y +k=0

This line is passes through the point ( -3,-3)

-(-3)+7(-3) +k=0

3 - 21 +k=0

-18 +k=0

k =18

The equation of the Perpendicular line to the given line is

-x +7y +18 =0