Parallel and Perpendicular Lines

Question

Write an equation of the line (in slope-intercept form) that is perpendicular to the line 2x+5y=-15 and contains the point (-8,3). 



Answer 1

Write an equation of the line (in slope-intercept form) that is perpendicular to the line 2x+5y=-15 and contains the point (-8,3). 



The line given is 2x+5y = -15

Which we can rewrite in y= mx+b form as

5y = -2x -15

Dividing by 5

y= - (2/5)x -3

So slope of this line is - (2/5)

A line perpendicular will have slope = (5/2) , Which is -(1/m)

Equation of new line will be

y = (5/2)x +b

Now we need to find b

Plug in Point (-8,3)

3 = (5/2) (-8) +b

3 = -20 +b

b= 23

Equation becomes y= (5/2)x +23

Answer 2

2x+5y = -15

5y = -2x-15

y = (-2/5)x - 3

the equation of the given line is -2/5

the perpendicular line has slope 5/2

B = y - mx = 3 - (5/2)(-8)

3 + 20

= 23

y = (5/2)x + 23

Answer 3

I would start by putting the given equation in slope-intercept form: y=mx+b.

2x+5y=-15 move 2x to the left side by subtraction

5y = -15 - 2x rearrange the 2x and -15

5y = -2x - 15 divide by 5

y = -2/5x - 3

Second, Identify what parts of the equation stay the same and what will change. For parallel, the slope, 2x, will stay the same. Now to make the line pass through the point (-8, 3). If you aren't drawing it out, then simply pug in the coordinates and solve for b.

y = -2/5x + b

3 = -2/5(-8) + b (to multiply I did -2/5 times -8/1. I usually leave this as is to make it more simple)

3 = 16/5 + b (to subtract I did 15/5 minus 16/5)

1/5 = b

The final answer for the parallel line is y = -2/5x + 1/5

To determine the equation for the perpendicular line, all you have to do is take the inverse of the slope and leave b the same.

The final answer for the perpendicular line is y=-5/2 + 1/5