Question

Graph y less than or equal to 3x

Answer 1

See Image Below.

Explanation:

The Shaded region is the area of numbers that this equation satisfies.

Answer 2

Please see attached image

Explanation:

In order to graph the inequality, start from plotting the boundary line defined by the equality;

y = 3 x

You just need two points to accomplish such. so let's use two simple values for x and find what the y-values are:

for x = 0 then y = 3 (0) = 0

for x = 1 then y = 3 (1) = 3

Then use the points (0, 0) and (1, 3) to plot the boundary line.

After this, grab any point on the plane either clearly above the boundary line, or clearly below it and check if the inequality satisfies. For example, you can pick the point (3, 0) which is on the x line, 3 units to the right of the origin, and clearly below the boundary line we just plot.

When you use it in the inequality, you get:

(0)
`\leq` 3 (3)

0
`\leq` 9

which is a true statement, therefore, the points below the boundary lie are also solutions of the inequality.

Then the solution consists of all the points in the boundary line we just plotted (and indicated by drawing a solid line), plus all the points below the line, as depicted in the attached image.