Question

help with Perpendicular and slope?

Answer 1

This is what you need to do:
1. Find the slope of the given line.
2. Find the slope of the perpendicular line.
3. Find the equation of the perpendicular.

Answer 2

How do I find the slope when its in Standard form?

Answer 3

1. If you rewrite the equation of the given line in the form

\( y = mx + b\)

then the slope is simply m.

All you need to do is solve the equation of the given line for y.

Answer 4

I tried that but I got stuck, here's what I had

2x + 4y = 5
÷4 ÷4
2x + y = 5/4

What do I do now?

Answer 5

\(2x + 4y = 5\)

First, you subtract the 2x term from both sides to move it to the right side.

\(4y = -2x + 5\)

Answer 6

Now you divide both sides by 4 to get y by itself.

Answer 7

2x + 4y = 5
-2x -2x
4y = -2x + 5
÷4 ÷4
y = -2/4x - 5/4

THat right?

Answer 8

+ 5/4 not negative

Answer 9

\(y = −\dfrac{2}{ 4} x+\dfrac{5}{ 4 } \)


Which can be reduced to:

\(y = −\dfrac{1}{2} x+\dfrac{5}{ 4 } \)


Now that we have the equation of the given line in the slope-intercept form,
\(y=\color{red}{m}x+b\) , it's easy to see what the slope, m, is:

\(y = \color{red}{−\dfrac{1}{2}} x+\dfrac{5}{ 4 } \)


m is the slope, so in our case, \(m=−\dfrac{1}{ 2} \).

Answer 10

So in order to make the other line perpendicular, the slope has to be 1/2x + 5/4?

Answer 11

Ok, we have done step 1. We know the slope of the given line is \(-\dfrac{1}{2} \).

2. Now we need to find the slope of the perpendicular line.

This is rhe rule you need to memorize:

\( \bf\color{red}{The ~slopes ~of ~perpendicular ~lines ~are ~negative ~reciprocals.} \)

Answer 12

Reciprocals are two number whose product is 1. Negative reciprocals are numbers whose product is -1.

Answer 13

That may sound complicated, but it is simple.

To find the reciprocal of a nunber, all you need to do is write the number as a fraction, and then flip the fraction.

To find the negative reciprocal of a number, write the number as a fraction, then flip the fraction, then change the sign.

Answer 14

We already have the slope of our line writen as a fraction, \( -\dfrac{1}{2} \).

To find the negative reciprocal, we flip the fraction and change the sign, so we get:
\(\dfrac{2}{1} \) which is simply 2.

The slope of the perpendicular is 2.

Answer 15

That concludes step 2. Now we know the slope of the perpendicular is 2.

Now we move on to step 3, finding the equation of the perpendicular line.

Answer 16

Are you following so far?

Answer 17

Yes, it makes sense to me so far thanks ^_^

Answer 18

Ok, let's do step 3.

3. The equation of a line in the slope-intercept form is

y = mx + b

We can use the slope we have, m = 2, and we can use the point we were given (-8, 2) in the equation. Then the only unknown will be b, the y-intercept.

Let's do that. Substitute -8 for x, 2 for y, and 2 for m.

We get this equation:

2 = 2(-8) + b

which we can solve easily for b.

Answer 19

2 = 2(-8) + b

2 = -16 + b

Add 16 to both sides:

18 = b

Answer 20

Now that we know b = 18, we can write the equation of the line in y = mx + b form:

y = 2x + 18

Answer 21

If you need the answer in standard form, then you can write it as:

y = 2x + 18

0 = 2x - y + 18

-18 = 2x - y

2x - y = -18

Answer 22

If the problem had asked for the equation of the line that is PARALLEL to the given line instead of perpendicular, then the only difference is that parallel lines have the same slope. That means, after finding the slope of the given line in step 1, then for step 2, you use the same slope. Then you move on to step 3 to find the equation of the parallel line.

Answer 23

Ohh okay, thank you Mathstudent! c: I appreciate it!

Answer 24

You're welcome.