slopes in parallel and perpendicular lines

Question

Write an equation of the line that passes through the point and is perpendicular to the graph of the given equation?

P(1,4); y = -2x + 4

P(5,3); y = 5x + 2

 

Write an equation of the line that passes through the point and is parallel to the graph of the given equation?

P(-1,3); y = -4x + 7

P(2,6); y = 2x + 1

 

Answer 1

Hi Lizzie,

 

  Write an equation of the line that passes through the point and is perpendicular to the graph of the given equation?
P(1,4); y = -2x + 4
P(5,3); y = 5x + 2

Write an equation of the line that passes through the point and is parallel to the graph of the given equation?
P(-1,3); y = -4x + 7
P(2,6); y = 2x + 1

 

 

Write an equation of the line that passes through the point and is perpendicular to the graph of the given equation?

The slope of a line that is perpendicular to a given line is the negative reciprocal.

 

P(1,4); y = -2x + 4

 

y=1/2x+b

 

To find b, substitute in the point.

4=1/2(1)+b

4=1/2+b

3.5=b

 

ANSWER:  y=.5x+3.5

P(5,3); y = 5x + 2

 

The perpendicular line would have a slope = -1/5

y=-1/5x+b

To find b, substitute in the point.

3=-1/5(5)+b

3=-1+b

4=b

 

ANSWER:  y=-1/5x+4

 

 

 

Second Question

Write an equation of the line that passes through the point and is parallel to the graph of the given equation?

 

Parallel lines have the same slope
P(-1,3); y = -4x + 7

 

y=-4x+b

To find b, substitute in the point.

3=-4(-1)+b

3=4+b

-1=b

 

ANSWER:  y=-4x-1

P(2,6); y = 2x + 1

 

y=-1/2x+b

To find b, substitute in the point.

6=-1/2(2)+b

6=-1+b

7=b

 

ANSWER: y=-1/2x+7

 

 

I hope this helps you with the process.