Graph of the solution set of the inequality

Which is a graph of the solution set of the inequality  3x - 4y ≤ 24?

A.)  

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C.)

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B.)

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D.)

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To graph 3x - 4y ≤ 24:
- first graph the boundary line, which is the graph of the equation 3x - 4y = 24, by getting it into
slope-intercept form y = mx + b

3x - 4y = 24
-4y = -3x + 24   {subtracted 3x from each side}
y = (3/4)x - 6   {divided each side by -4}
slope is 3/4
y-intercept is -6

To graph the line y = (3/4)x - 6
- put a point on -6 on the y-axis  {the y-intercept}

- from there, move up 3 and to the right 4 and put another point   {using the slope}

- draw a solid line through the two points, since it is a ≤ sign in the original inequality

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Change 3x - 4y ≤ 24 to "slope-intercept form" to determine which direction the shading goes.
3x - 4y ≤ 24
-4y ≤ -3x + 24   {subtracted 3x from each side}
y ≥ (3/4)x - 6   {divided each side by -4 and changed the inequality sign since dividing by a negative}

Since the inequality sign is ≥, within slope-intercept form, then shade above the boundary line.

C.)













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