Question

Select the correct answer. Choose the system of Inequalities that best matches the graph below. y 5 4 X 1 6 41 O A. y < 2x ya

Answer 1

First, we have to find the equation of the blue and red lines.

Blue line.

Let's use the points (-3, 0) and (0, 1). We use the slope formula.

`m=(y_2-y_1)/(x_2-x_1)`

Replacing the points, we have.

`m=(1-0)/(0-(-3))=(1)/(3)`

The equation of the blue line is

`y=(1)/(3)x+1`

Red line.

Let's use the points (1,1) and (2,3).

`m=(3-1)/(2-1)=(2)/(1)=2`

The equation of the red line is

`y=2x-1`

Then, we find the inequality signs for each equation. Notice that the area of the solution is above the blue line and on top of the red line.

So, the inequalities are

`\begin{gathered} y\leq(1)/(3)x+1 \\ y\ge2x-1 \end{gathered}`