Question

what is the graph of the inequality-3y≥7x-6

Answer 1

The first step to graph this inequality is solving it for y:

$\begin{gathered} -3y\ge7x-6 \\ 3y\le-7x+6 \\ y\le\frac{-7x+6}{3} \\ y\le-\frac{7}{3}x+2 \end{gathered}$

Then, we need to find two points of the equivalent equation:

$\begin{gathered} y=-\frac{7}{3}x+2 \\ x=0\colon \\ y=-\frac{7}{3}\cdot0+2 \\ y=0+2 \\ y=2 \\ \\ x=3\colon \\ y=-\frac{7}{3}\cdot3+2 \\ y=-7+2 \\ y=-5 \end{gathered}$

The two points are (0, 2) and (3, -5).

Graphing this equivalent equation, we have:

Now, to graph the inequation, we use this line, and graph all values below the line (because the sign is "lesser than or equal").

Also, since the line is part of the solution, we keep the line filled and not dashed.

So the graph of the inequation is the following: