Which inequality matches the graph? X, Y graph. X range is negative 10 to 10, and y range is negative 10 to 10. Dotted line on g

Question

Which inequality matches the graph?

X, Y graph. X range is negative 10 to 10, and y range is negative 10 to 10. Dotted line on graph has positive slope and runs through negative 3, negative 8 and 1, negative 2 and 9, 10. Above line is shaded.

−2x + 3y > 7
2x + 3y < 7
−3x + 2y > 7
3x − 2y < 7

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niczorrrr 3 years 2021-08-02T16:44:27+00:00 1 Answers 76 views 0

Answers ( )

  1. Sigrid
    0
    2021-08-02T16:45:34+00:00
    Reply

    Given:

    The dotted boundary line passes through the points (-3,-8), (1,-2) and (9,10).

    Above line is shaded.

    To find:

    The inequality for the given graph.

    Solution:

    Consider any two points on the line. Let the two points are (1,-2) and (9,10). So, the equation of the line is:

    y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

    y-(-2)=\dfrac{10-(-2)}{9-1}(x-1)

    y+2=\dfrac{10+2}{8}(x-1)

    y+2=\dfrac{12}{8}(x-1)

    y+2=\dfrac{3}{2}(x-1)

    Multiply both sides by 2.

    2(y+2)=3(x-1)

    2y+4=3x-3

    2y-3x=-3-4

    -3x+2y=-7

    Above line is shaded and the boundary line is a dotted line. So, the sign of inequality must be >.

    -3x+2y>-7

    This inequality is not in the equations. So, multiply both sides by -1 and change the inequality sign.

    (-3x+2y)(-1)<-7(-1)

    3x-2y<7

    Therefore, the correct option is D.

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