20 points Choose the system of inequalities that best matches the graph below

D

Step-by-step explanation:

To find the system of inequalities, we simply need to find the equation of each line.

Thus, let's find the inequality that is represented by each line.

Red Line:

First, let’s determine the slope. To do so, we can use the slope formula:

We can use any two points that's on the Red Line. Using (0, 1) and (1, 3) and substituting them into the slope formula yields:

Therefore, the slope of the red line is two.

To write the equation of the red line, we can use the slope-intercept form:

Notice that our y-intercept of our red line is (0, 1). Therefore, b = 1 and we already determind that m = 2:

Now, we need to determine our sign. Notice that the shaded region is below the red line. Therefore, y is less than our equation.

And since our line is shaded, our sign will be less than or equal to. Therefore:

Blue Line:

Again, let’s first find the slope. We can use the two points (0, 2) and (2, 3). Hence:

So, the slope is 1/2.

We can now use the slope-intercept form. Notice that our y-intercept is (0, 2). Thus, we will substitute 1/2 for m and 2 for b. This yields:

Finally, we will determine our sign. Since the shaded region is above the blue line, our y is greater than our equation. And since it’s shaded, our sign is greater than or equal to. Therefore, our equation is:

Thus, all together, our inequalities are:

Therefore, our answer is D

a is the best answer choice