How do you graph the inequality #-2x - 4y ≤ 8#?

Question

Genesis Allen · Accepted Answer

See step below in the explanation: you would plot #y=-1/2x-2# and shade the area where #y > -1/2x-2#

What we will do, is first, graph the "equals" line, then shade in the correct area.

There are three steps to do this:

Rearrange the equation so "y" is on the left and everything else on the right.
Plot the "y=" line
Shade above the line for a "greater than" (y≥).

In our instance: 1) Rearrange the equation so "y" is on the left: #-2x-4y<=8 -> 4y>=-2x-8 -> y>=-1/2x-2#

2) Plot the #y=-1/2x-2# line:

graph{y=-1/2x-2 [-7.9, 7.9, -3.95, 3.95]}

Shade above the line for a "greater than" (y≥):

graph{y>=-1/2x-2 [-7.89, 7.91, -3.95, 3.95]}

Abigail Allen · Answer

undefined To graph the inequality $ -2x - 4y \leq 8 $, follow these steps:

1. Start by graphing the boundary line $ -2x - 4y = 8 $. To do this, rewrite the equation in slope-intercept form: $ y = -\frac{1}{2}x - 2 $.
2. Plot the y-intercept at (0, -2), and then use the slope to find additional points. The slope is -1/2, which means that for every 1 unit increase in x, y decreases by 1/2 unit.
3. Draw a dashed line through the plotted points. Since the inequality includes "less than or equal to" ($\leq$), the boundary line should be dashed to indicate that the points on the line are included in the solution set.
4. Lastly, decide which side of the boundary line to shade. To do this, choose a test point not on the line, such as (0,0). Substitute the coordinates into the original inequality: $ -2(0) - 4(0) \leq 8 $. Simplify to see if the statement is true or false. If true, shade the side of the boundary line containing the test point. If false, shade the other side.

This process will create the shaded region representing the solution set for the inequality.