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Math Help - Simple Calculus

  1. #1
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    Simple Calculus

    Find an equation for the line through (4,-1) and perpendicular to the line through (-2,3) and (3,7).

    Please provide all steps as im very confused about what to do
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  2. #2
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    Quote Originally Posted by fvaras89 View Post
    Find an equation for the line through (4,-1) and perpendicular to the line through (-2,3) and (3,7).

    Please provide all steps as im very confused about what to do

    first of all find the gradient for the points (-2,3) and (3,7).

    m= \frac{y_2-y_1}{x_2-x_1} = \frac{7-3}{3-(-2)} = \frac{4}{5}

    perpendicualr gradient is \frac{-1}{m} = \frac{-1}{\frac{4}{5}} = \frac{-5}{4}

    So the line y=mx+c for the perpendicular becomes y=\frac{-5}{4}x+c

    Now use (4,-1) to find c and you will have your answer....
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  3. #3
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    Thank you so much!!

    Is it alright to have the final equation as

    y+1 = -5/4 (x-4)?
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  4. #4
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    Its ok, depends what form you are asked to provide your answer in.

    Your answer is in the form y-y_1 = m(x-x_1) which is fine.

    If you need to find the y-intercept which is common you would need to find c as follows

     y=\frac{-5}{4}x+c

     -1=\frac{-5}{4}\times 4+c

     -1=-5+c

     c=4 \Rightarrow y=\frac{-5}{4}x+4
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