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

__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

**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.)**

*- Algebra House*