# Thread: Finding the equation of lines

1. ## Finding the equation of lines

A bit confused on this:

1. Find the equation of the line between the points (9, -9) and (-5, -2).

m=y2-y1 -2 - -9 7 = -1
--------- (over) --------- ---- ----
x2-x1 -5 - -9 -14 2

y=-1/2x+b ... How would I find b, the y-intercept then?

2. Find the equation of the line with an x-intercept of -2 and a y-intercept of 7.

That's the points (-2, 0) and (0, 7), so m=y2-y1/x2-x1 again, or 7-0/0--2 = 7/2....which would be y=7/2x+b and the y-intercept is 7 so the final equation would be y=7/2x+7 ? just checking.

3. Find the equation of the line that has the same x-intercept as x-4y=3 and the same y-intercept as 2x-3y=9.

x-4y=3 rearranges to x=4y+3, and to find the x-int you would substitute 0 in right for y so x=4(0)+3 or x=4+3, or x=7... so the x-intercept is 7.

For the y-intercept, 2x-3y=9 you substitute 0 in for x, so 2(0)-3y=9 would be 0-3y=9 or just -3y=9... or y=-3.

I guess the equation so far would be y=mx-3... but I don't know how I would find the slope at this point to finish the equation.

4. Finally... (the most important question) If A(1,2), B(-2,5) and C(3, 4), find the equation of the line perpendicular to AB and through C.

I know the slope of the line perpendicular to something is the negative reciprocal... but I don't know what to do here.

If I found the slope of A and B, that would be 2-5/-2-1 or -3/-3 or 1 I guess, so then would the slope of the new line be -1/2? What impact does "through C" have? The equation so far if that's right of the new line would be y=-1/2x+b... b being the y-intercept again, but I don't know what to do from this point on.

Thanks for reading! My math skills aren't great... or even "good" for that matter

2. Q1 is to mashed up for me to understand.

Originally Posted by ~NeonFire372~
A bit confused on this:

1. Find the equation of the line between the points (9, -9) and (-5, -2).

m=y2-y1 -2 - -9 7 = -1
--------- (over) --------- ---- ----
x2-x1 -5 - -9 -14 2

y=-1/2x+b ... How would I find b, the y-intercept then?

2. Find the equation of the line with an x-intercept of -2 and a y-intercept of 7.

That's the points (-2, 0) and (0, 7), so m=y2-y1/x2-x1 again, or 7-0/0--2 = 7/2....which would be y=7/2x+b and the y-intercept is 7 so the final equation would be y= (7/2) x + 7 ? just checking. Mr F says: Correct. Note the brackets ....

3. Find the equation of the line that has the same x-intercept as x-4y=3 and the same y-intercept as 2x-3y=9.

x-4y=3 rearranges to x=4y+3, and to find the x-int you would substitute 0 in right for y so x=4(0)+3 or x=4+3, or x=7... so the x-intercept is 7. Mr F says: 4(0)+3 = 0 + 3 = 3.

For the y-intercept, 2x-3y=9 you substitute 0 in for x, so 2(0)-3y=9 would be 0-3y=9 or just -3y=9... or y=-3. Mr F says: Correct.

I guess the equation so far would be y=mx-3... but I don't know how I would find the slope at this point to finish the equation. Mr F says: Substitute (3, 0) into y = mx - 3 and solve for m.

4. Finally... (the most important question) If A(1,2), B(-2,5) and C(3, 4), find the equation of the line perpendicular to AB and through C.

I know the slope of the line perpendicular to something is the negative reciprocal... but I don't know what to do here.

If I found the slope of A and B, that would be 2-5/-2-1 or -3/-3 or 1 Mr F says: NO. (2 - 5)/(1 -(-2)) = -3/3 = -1.

I guess, so then would the slope of the new line be -1/2? Mr F says: No. The gradient of the perpendicular is (and you should know this) the negative reciprocal of -1, that is, 1.

What impact does "through C" have? The equation so far if that's right of the new line would be y=-1/2x+b... b being the y-intercept again, but I don't know what to do from this point on.

Mr F says: Substitute m = 1 to get the required equation as y = x + c. Now substitute the given point (3, 4) and solve for c.

Thanks for reading! My math skills aren't great... or even "good" for that matter
..

3. Sorry, I tried to write question 1 but I guess the formatting didn't work out right...

It's Find the equation fo the line between the points (9, -9) and (-5, -2)... so I tried to find the slope, which is m=y2-y1/x2-x1 or -2 - -9/-5-9 or 7/-14 or -1/2... so the equation so far is y=mx+b - y=-1/2x+b, but I don't know how to find b, the y-intercept.

4. Originally Posted by ~NeonFire372~
Sorry, I tried to write question 1 but I guess the formatting didn't work out right...

It's Find the equation fo the line between the points (9, -9) and (-5, -2)... so I tried to find the slope, which is m=y2-y1/x2-x1 or -2 - -9/-5-9 or 7/-14 or -1/2... so the equation so far is y=mx+b - y=-1/2x+b, but I don't know how to find b, the y-intercept.
Two choices:

Substitute (9, -9) into y = -(1/2) x + b and solve for b.

Substitute (-5, -2) into y = -(1/2) x + b and solve for b.

5. Originally Posted by mr fantastic
Two choices:

Substitute (9, -9) into y = -(1/2) x + b and solve for b.

Substitute (-5, -2) into y = -(1/2) x + b and solve for b.
Thanks again for the help. That was so obvious but didn't come to mind for some reason.

I just tried the last question you helped with (the find the equation of the line perpendicular to AB and through C one), it ended off with y=1x+b right, 1 being the slope, so I substituted it in like this:

4=1(3)+b
4=3+b
1=b

The final equation being y=1x+1

Is that right? Just making sure. Thanks again!

6. Originally Posted by ~NeonFire372~
Thanks again for the help. That was so obvious but didn't come to mind for some reason.

I just tried the last question you helped with (the find the equation of the line perpendicular to AB and through C one), it ended off with y=1x+b right, 1 being the slope, so I substituted it in like this:

4=1(3)+b
4=3+b
1=b

The final equation being y=1x+1

Is that right? Just making sure. Thanks again!
Looks OK. I'd write it as y = x + 1.

7. Thanks for all the help!

Edit: My final answer for 1 is y=-1/2x - 9 is that right?