Question

Which is a graph of the solution set of the inequality 3x-4y\le24?

Answer 1

Graph #4

Step-by-step explanation

To graph this inequality, we can solve it for y to obtain the equation of the line. First, subtract 3x from both sides of the inequality,

`\begin{gathered} 3x-3x-4y\le-3x+24 \\ -4y\le-3x+24 \end{gathered}`

And divide both sides by -4. Remember that when we multiply or divide both sides of an inequality by a negative value, we have to flip the inequality sign,

`\begin{gathered} (-4y)/(-4)\ge(-3x+24)/(-4) \\ y\ge(3)/(4)x-6 \end{gathered}`

Thus, the solution set of this inequality is the line y = 3/4x - 6 and all points above the line. Note that the line has a positive slope, so the graphs can only be the second or fourth, and only on the fourth graph, the shaded area is above the line.