line a passes through the points (3,4) and (-1,2). line b passes through the points (-12,0) and (-6,-4). at what point do the lines intersec

Question

line a passes through the points (3,4) and (-1,2). line b passes through the points (-12,0) and (-6,-4). at what point do the lines intersect

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RuslanHeatt 2 months 2021-07-30T08:36:52+00:00 1 Answers 3 views 0

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    2021-07-30T08:38:48+00:00

    Answer:

    The point of intersection of the two lines is;

    (-9,-2)

    Step-by-step explanation:

    What we have to here is to get the equation of both lines, solve simultaneously and get the intersection points

    For the first line;

    The general form is

    y = mx + b

    formula for the slope is;

    m = (y2-y1)/(x2-x1)

    The points (3,4) and (-1,2)

    m = (2-4)/(-1-3) = -2/-4 = 1/2

    So the equation is;

    y = 1/2x + b

    To get b, let us substitute coordinates of the first point;

    4 = 1/2 * 3 + b

    4 = 3/2 + b

    b = 4 – 3/2

    b = (8-3)/2 = 5/2

    So the equation is;

    y = 1/2x + 5/2

    For the second line;

    Slope;

    m = (-4-0)/(-6+12) = -4/6 = -2/3

    The equation is;

    y = -2x/3 + b

    Let us substitute the first

    0 = -2/3(-12) + b

    0 = 8 + b

    b = -8

    The equation is;

    y = -2x/3 – 8

    Now , we want to get the intersection point

    To do this, we have to solve both equations simultaneously;

    Since we have an expression for y in both cases, let us equate both y

    -2x/3-8 = 1/2x + 5/2

    Multiply through by 6

    -4x – 48 = 3x + 15

    -4x-3x = 15 + 48

    -7x = 63

    x = 63/-7

    x = -9

    To get x;

    Recall;

    y = -2x/3 – 8

    y = -2/3(-9) – 8

    y = 6 – 8

    y = -2

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