# Finding the equation of lines

• Sep 24th 2009, 04:55 PM
~NeonFire372~
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 (Giggle)
• Sep 25th 2009, 03:12 AM
mr fantastic
Q1 is to mashed up for me to understand.

Quote:

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 (Giggle)

..
• Sep 25th 2009, 04:24 AM
~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.
• Sep 25th 2009, 04:52 AM
mr fantastic
Quote:

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.
• Sep 25th 2009, 05:15 AM
~NeonFire372~
Quote:

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!
• Sep 25th 2009, 05:18 AM
mr fantastic
Quote:

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.
• Sep 25th 2009, 05:21 AM
~NeonFire372~
Thanks for all the help! :)

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