Question

4x + 2y > 8 Graph the inequality and explain your steps.

Answer 1

Let's begin by listing out the information given to us:

4x + 2y > 8

Let's make y the subject of the equation to resemble the general equation,

y = mx + b. We have:

2y > -4x + 8

divide through all variables & constant by 2, we have:

y > -2x + 4

Let's change > to = to test some points

y = -2x + 4

When (x, y) = (0, 0), we have:

0 = -2(0) + 4

0 > 4 (FALSE)

y > -2x + 4; m = -2

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ when\text{ x= 2} \\ -2=\frac{y-0}{2_{}-0}\Rightarrow y_{}=-4 \\ \text{when x = -2} \\ -2=(y-0)/(-2-0)\Rightarrow y=4 \\ \text{when x = -5} \\ -2=(y-0)/(-5-0)\Rightarrow y=10 \\ \text{when x = 5} \\ -2=(y-0)/(5-0)\Rightarrow y=-10 \end{gathered}`

We plot this points on a graph, we have (image attached)