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Math Help - Finding the equation of lines

  1. #1
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    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
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  2. #2
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    Q1 is to mashed up for me to understand.

    Quote Originally Posted by ~NeonFire372~ View Post
    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
    ..
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  3. #3
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    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.
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  4. #4
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    Quote Originally Posted by ~NeonFire372~ View Post
    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.
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    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!
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  6. #6
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    Quote Originally Posted by ~NeonFire372~ View Post
    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.
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  7. #7
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    Thanks for all the help!

    Edit: My final answer for 1 is y=-1/2x - 9 is that right?
    Last edited by ~NeonFire372~; September 25th 2009 at 06:57 AM.
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