Question

Graph the linear inequality shown below on the provided graph. y < 1/3 x - 6

Answer 1

First of all, we have to draw the line. To draw a line, we only need two points. To sample to points, we choose two arbitrary x values, and compute the correspondent y values.

We may choose x=0 and x=3 to make computation/drawing easier. We have

$f(x)=\dfrac{1}{3}x-6 \implies f(0)=\dfrac{1}{3}\cdot 0-6=-6$

$f(x)=\dfrac{1}{3}x-6 \implies f(3)=\dfrac{1}{3}\cdot 3-6=1-6=-5$

So, this line passes through the points (0, -6) and (3, -5). Draw these two points and connect them: you have the line

$y=\dfrac{1}{3}x-6$

Now, to solve the inequality

$y$

recall that smaller values for y means "below" in the coordinate axes. So, every point that lies below the line is a solution to the inequality.