Question

Find equation of the line thats perpendicular to the line 2x +5y+8=0 that passes through the line (-1,-2)

Answer 1

You know how to find the slope of the given line @jessgrabbinn ???

Answer 2

y= -2/5x ??

Answer 3

How'd you get that?

Answer 4

y= mx+b
since the line is 2x+5y+8=0
you would rearrange the formula
5y =-2x -8
y= -2/5x -8/5

am i right?

Answer 5

Yeah. And perpendicularity means negative reciprocal of the original slope. Then, what is our new slope?

Answer 6

Hint. Find the slope of the equation 2x +5y+8=0 by transforming it into y=mx + b

Answer 7

@jessgrabbinn , are you there?

Answer 8

y= 2/5x + 8/5 ?

Answer 9

or are you referring to the original line?

Answer 10

it would be y= -2x/5 - 8/5
so the slope is -2/5
This is the crucial point: Since the equation of the line that you are finding for is perpendicular, the product of their slopes would be equal to -1 or in other words, their slope is negative reciprocal of one another

Answer 11

Yes. The slope of the perpendicular line is actually the negative reciprocal of the slope of the original line. Get it @jessgrabbinn ??

Answer 12

Is that my answer? or do I keep going?

Answer 13

So, the slope of the perpendicular line will be 5/2.
And upon using the point slope form.
y -y1 = m (x-x1)
y +2 = 5/2 (x+1)
And there you will find the new line that is perpendicular to the original line. :)

Answer 14

so the slope of the perpendicular line would be 5/2
then use the point slope form y-y1=m (x-x1)
substitute the point (-1,-2)
it will become y-(-2) = 5/2 [x-(-1)]
simplify: y + 2 = 5/2 (x+1)
multiply 2 to both sides
2y + 4 = 5 (x+1)
2y + 4 = 5x + 5
General form of equation is 5x - 2y +1 = 0

Answer 15

can yuo follow @jessgrabbinn ??

Answer 16

why did you multiply 2 to both sides?

Answer 17

@jessgrabbinn that is to remove the denominator in the right side and make the equation simplier

Answer 18

\[y+2=\frac{ 5 }{ 2 } (x+1)\]
to simplify this
\[2[y+2=\frac{ 5 }{ 2 } (x+1)]\]
So we will have
\[2y+4 = 5x + 5\]
Hence, the general form will be
\[5x-2y+1 = 0\]
Are you englihtened now?

Answer 19

Notice that 5/2 (x+1) became 5 (x+1) because the denominator is cancelled

Answer 20

OH gotcha, I'm still a little confused on what happened here:
" multiply 2 to both sides
2y + 4 = 5 (x+1)
2y + 4 = 5x + 5
General form of equation is 5x - 2y +1 = 0"

why is it 5x+5 ?

Answer 21

how did 5/2x +1 suddenly become 5x+5?

Answer 22

The 2 is already eliminated in the right side, right? Hence, what is left is 5(x+1) = 5x+5

Answer 23

where did the 5 come from?
after you multiply each side by 2, doesnt it become 2y+4=5x+2 ?

Answer 24

We actually used distributive property. 5(x+1) = (5x)+(5*1)

Answer 25

OH

Answer 26

after you use the distributive prop, shouldnt it become 2y+4=5x+10?

Answer 27

after you multply by 2

Answer 28

No. The reason why we multiply it by 2 is that to eliminate the 2 in the denominator. Hence. 5x+5 remains still.