Question

2. Graph the following inequality on the axes provided below: 6x + 2y = 8 -10 8 6 4 2 -101-8-6 1-4-2 -2 2 4_LG_L 8 10 -4 -6 -8 -10 True or False: (1,1) is a solution to the inequality. Explain using evidence from your graph.

Answer 1

We are given the following inequality

`6x+2y<8`

Let us first convert the inequality into slope-intercept form

`\begin{gathered} 6x+2y<8 \\ 2y<-6x+8 \\ y<-(6x)/(2)+(8)/(2) \\ y<-3x+4 \end{gathered}`

Comparing this inequality with the standard slope-intercept form we see that

Slope = -3 and y-intercept = 4

So the graph of the inequality is

The area left to the red line represents the solution of the inequality.

Now we need to check if the point (1, 1) lies left to the red line.

We can clearly see that point (1, 1) is just left to the red line hence it is a solution.

Therefore, it is true.