Find the point-slope equation for the line that passes through the points (5,19) and (-5,-1).

Question

Find the point-slope equation for the line that passes through the points (5,19) and (-5,-1).

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Raelynn 4 weeks 2021-12-27T12:31:51+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-12-27T12:33:09+00:00

    Answer: y – 19 = 2(x – 5)

    Step-by-step explanation:

    The point slope form is expressed as

    y – y1 = m(x – x1)

    Where

    m represents slope

    Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

    change in the value of y = y2 – y1

    Change in value of x = x2 -x1

    y2 = final value of y

    y 1 = initial value of y

    x2 = final value of x

    x1 = initial value of x

    The given points are (5,19) and (-5,-1)

    y2 = – 1

    y1 = 19

    x2 = – 5

    x1 = 5

    Slope,m = (- 1 – 19)/(- 5 – 5) = – 20/- 10 = 2

    To determine the equation, we would substitute x1 = 5, y1 = 19 and m= 2 into the point slope form equation. It becomes

    y – 19 = 2(x – 5)

    0
    2021-12-27T12:33:36+00:00

    The equation for the slope of a line defined by 2 points, (X1, Y1) and (X2, Y2) is:

    (Y2-Y1)/(X2-X1) = (-1-19)/(-5-5) = -20/-10 = 2

    The equation of a line is y = mx + b where m is the slope of the line and b is the y-intercept. We know the slope is 2 so we can re-write the equation as:

    Y = 2x + b and we can solve for the y-intercept, which is the point where the line crosses the y axis, by putting the xy coordinates from either point (5, 19) or (-5, -1) into the equation:

    19 = (2)(5) + b if we use first coordinates

    or

    -1 = (2)(-5) + b if we use 2nd coordinates

    B = 9 in both cases so now our y = mx+b equation becomes:

    Y=2x + 9

    You can check this by putting in a single x or y coordinate and the equation will yield the other pair of that coordinate.

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