What is the equation ?

What is the equation based on the graph below. 

Attachment image

2 Answers

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  • 1 month ago

    Two points on dashed line: (0, -3) and (2, 7).

    Slope of dashed line = (7 - (-3)) / (2 - 0) = 10 / 2 = 5

    Y-intercept: (0, -3)

    y = mx + b

    y = 5x - 3 is equation of dashed line.

    Trying (0, 0), in the shaded region, gives 0 > -3

    So, the shaded region is represented by y > 5x - 3.

  • 1 month ago

    Let's start with the line.  We want something in the form of:

    y = mx + b

    The x-intercept is (0, -3), so b = -3:

    y = mx - 3

    Now we look at the slope.  I think of it as "rise over run".  So starting with (0, -3), find the next point on the line where we can find it on the grid.  I see point (1, 2).  The "rise" is 5 and the "run" is 1, so the slope is:

    m = 5/1

    m = 5

    Now the equation is:

    y = 5x - 3

    Now we need to look at it as an inequality.  You want to see if the shaded region is above the line (>) or below the line (<)

    The shaded region is above the line, so the inequality is now:

    y > 5x - 3

    Finally, we look at if the line is solid or dashed.  If it's solid, the solution includes the points on the line (≥) and if dashed the line does not include solution data points (>).  It is dashed, so the solution is:

    y > 5x - 3

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