Step-by-step explanation:
Given the inequality statement, 2x + 4y ≤ 8:
In order to graph the given inequality statement, we must first transform this into its slope-intercept form, y = mx + b.
Start by setting the inequality statement into an equation by substituting the
"≤" into "=."
2x + 4y = 8
Next, subtract 2x from both sides:
2x + 4y = 8
2x -2x + 4y = - 2x + 8
4y = -2x + 8
Then, divide both sides by 4 to isolate y:
[tex]\displaystyle\mathsf{\frac{4y}{4}\:=\:\frac{-2x\:+\:8}{4}}[/tex]
y = -½x + 2 ⇒ This is the slope-intercept form
Graphing the line
We can graph the line using the equation. Start by plotting the y-intercept, (0, 2), and use the slope (m = -½) to plot other points on the graph. Use a solid boundary line due to the "≤" symbol.
Shading the solution region
Next, we must choose test point that is not on the line. The purpose of the test point is to determine which part of the half-plane region to shade. Let's use the point of origin, (0, 0) as our test point, and substitute its values into the inequality statement:
2x + 4y ≤ 8
2(0) + 4(0) ≤ 8
0 + 0 ≤ 8
0 ≤ 8 (True statement).
Therefore, we must shade the half-plane region that contains the test point.
Attached is a screenshot of the graphed linear inequality.
