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.

$m=\frac{y_2-y_1}{x_2-x_1}$

Replacing the points, we have.

$m=\frac{1-0}{0-(-3)}=\frac{1}{3}$

The equation of the blue line is

$y=\frac{1}{3}x+1$

Red line.

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

$m=\frac{3-1}{2-1}=\frac{2}{1}=2$

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

$\begin{gathered} y\leq\frac{1}{3}x+1 \\ y\ge2x-1 \end{gathered}$