Question

Indicate the equation of the given line in standard form.The line through point (-3, 4) and perpendicular to a line that has slope 2/5

Answer 1

Okay, this is pretty much like before, we have a point (a,b), but we don't have a slope m... yet...

right?

Answer 2

right.

Answer 3

But we have the necessary information to get the slope... we know that it's perpendicular to a line with slope 2/5

Following me so far?

Answer 4

kinda.

Answer 5

Please be sure, and if there's anything you don't understand, tell me :D

Answer 6

ok. i sorta just needed to reread the question.

Answer 7

Okay.... tell me when you're ready to proceed.

Answer 8

oh ok i see where it says its perpendicular. im ready to go on.

Answer 9

Okay, when two lines are perpendicular, their slopes, say m1 and m2 have this property...
\[\Large m_1m_2 =-1\]

Answer 10

Everything okay so far?
(Tell me if I'm being too slow)

Answer 11

yeah. get it.

Answer 12

Okay, so we need the slope of our line, while only knowing that it is perpendicular to a line with slope 2/5.

So let's let m be our missing slope
And we have this relation
\[\Large \frac25\color{green}m = -1\]
Can you solve for m?

Answer 13

i dont understand how to solve for m.

Answer 14

Okay, let me put it this way instead...
If you have a line which is perpendicular to another line with a known slope ...

then...

Answer 15

What you do with that slope is flip it around, and then multiply by -1.

So in this case, our line is perpendicular to a line of slope 2/5

So to get the slope of our line, we flip around 2/5, giving us 5/2

and then multiply it by -1


So the slope m of our line is given by
\[\Large \color{green}m = \color{green}{-\frac25}\]

Answer 16

Sorry, my bad...
\[\Large \color{green}{m}=\color{green}{-\frac52}\]

Answer 17

oh ok... you must have a lot of patience.

Answer 18

quite :D

so we now have a slope m
We have values for a and b... what are they?

Answer 19

-3 & 4

Answer 20

That's right :D
So... recap
\[\large \color{green}m = \color{green}{-\frac52}\]\[\large\color{red}{a}= \color{red}{-3}\]\[\large \color{blue}{b}= \color{blue}4\]

Just plug them into our equation....
(Please do remember this form)
\[\Large y = \color{green}m(x-\color{red}a)+\color{blue}b\]

Answer 21

@Grimmlockhart stuck?

Answer 22

I have to go now, though, if you still have questions, I'm sure there are plenty of people here who can assist you :)
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Terence out