Looking at two linear inequalities, 5𝑥−2𝑦<10 and 𝑦≤𝑥, how can you identify the x-intercept of boundary and y-intercept of boundary for equation (1). Also, identify the graph of inequality equation ( 1) as a solid line or a dashed line. Lastly, provide the procedural steps how to graph these inequalities.

Your initial response should be 100-200 words in length

Discussion Board Reply

Reply from K. Gray

To find the x-intercept of the boundary for the equation 5x – 2y < 10, we set y = 0 and solve for x:

5x – 2(0) = 10

5x = 10

x = 2

So, the x-intercept is at (2, 0).

To find the y-intercept of the boundary, we set x = 0 and solve for y:

5(0) – 2y = 10

-2y = 10

y = -5

Therefore, the y-intercept is at (0, -5).

The graph of the inequality 5x – 2y < 10 will have a dashed line because the inequality does not include the equal sign.

To graph these inequalities:

1. Start by graphing the line 5x – 2y = 10. To find the x-intercept, set y = 0 and solve for x. To find the y-intercept, set x = 0 and solve for y. Plot these points and draw a dashed line through them.

2. Next, graph the line y = x. This line is a solid line because the inequality includes the equal sign.

3. Choose a test point not on the line. For example, (0,0) is a common choice.

4. Substitute the test point into each inequality. If it’s true, shade the region that contains the test point. If it’s false, shade the other region.

5. The solution to the system of inequalities is the overlapping shaded region.