Question

(25 points!!!!) draw the graph of the area bounded by these inequalities

Answer 1

Step-by-step explanation:

To draw the graph, follow these steps:

1. Graph the lines using points from the equations. (the blue line shown should be dotted, unfortunately I cannot do that in the program I used)
2. Determine which direction the inequalities are correct.  
3. Find the boundary given.

The three inequalities given form a triangle.

The first equation, y ≤ 2x + 5, has a y-intercept at (0, 5) and a point at (-2, 1).

The second equation, y < -3x + 10, has points at (3, 1) and (2, 4).

Use two points to draw the lines.

After the lines are drawn, determine which side of the line the inequality works on. You can do this by testing points that are not on the line.

I will test each inequality using (0, 1):

y ≤ 2x + 5

0 ≤ 2 + 5

This is correct, so the inequality for y ≤ 2x + 5 will be shaded towards (0, 1).

y < -3x + 10

0 < -3 + 10

This is correct, so the inequality for y < -3x + 10 will be shaded towards (0, 1).

0 ≤ 1

This is correct, so the inequality for 0 ≤ y will be shaded upwards towards (0, 1).

The end result of this graph is all three inequalities being shaded (inwards).

The solution is a triangle with points at (1, 7), (3.33333, 0), and (-2.5, 0).