Question

What is the equation of the line that passes through (4, -1) and (-2, 3)?

Answer 1

oh thats easy...just plug it in to y=mx+b i think

Answer 2

Well first...we need to find slope

you have 2 points

(4, -1) (-2, 3)
(x1,y1)(x2,y2)

plug those (using the labeling I provided below the points) into this equation

\[m = \frac{ y2 - y1 }{ x2 - x1 }\]

This will be your slope of the line

Answer 3

-2x + 3y - 5 = 0 is this correct

Answer 4

not quite...you can always check your answer by plugging in a point that you were given and checking if it works...in that case

-2(4) + 3(-1) - 5 = 0
-8 -3 -5 =0
-16 = 0
Doesn't work...

Try it the way I have explained above...by finding the slope first

Answer 5

m=4/-2 ?

Answer 6

close

3 - (-1) 4
------- = ------
-2 - 4 -6

When simplified becomes -2/3

right?

Answer 7

that's what i had the first time but it didn't seem right, but i guess it is

Answer 8

never second guess yourself :)

but okay....That is your 'm'

Now, pick which of the 2 point you were given...that you would like to use...

Answer 9

4,-1

Answer 10

okay

Using this equation

y = mx + b

'y' will be the y-value in the point you chose
'x' will be the x-value in the point you chose
'm' will be the slope we just found

so

after plugging everything in

-1 = (-2/3)(4) + b

Solve for b

Answer 11

is B, the next point?

Answer 12

'b' is what we're solving for...and this will be the y-intercept of your lines equation...Once you solve for 'b' here...you will have your full equation as you will see...

Answer 13

to solve you do multiply -2/3 and 4

Answer 14

Yes you can start there....after you do that you will have

-1 = (-8/3) + b

What would we do next?

Answer 15

would it be -2
or 2

Answer 16

not quite

next you would add (8/3) to both sides to cancel it out on the right side

-1 + (8/3) = b

finish simplifying that left side

what is -1 + (8/3)?

Answer 17

7/3

Answer 18

not quite....you need to find a least common denominator when adding or subtracting fractions

the lcd here...would be 3...so you need to multiply -1 by (3/3)

this will give you

-3 8
--- + ---
3 3

now you can combine the fractions and you'll get

-3 + 8
------
3

what does this simplify to?

Answer 19

5/3

Answer 20

perfect....that is your y-intercept

Now....you have everything you need for your line equation

you have a slope (-2/3)
and
you have a y-intercept (5/3)

putting that all together you get

\[y = -\frac{ 2 }{ 3 }x + \frac{ 5 }{ 3 }\]

That would be the equation of your line

Answer 21

THanks!

Answer 22

No problem! I hope it was understandable?