Question

Linear Inequality

Answer 1

Answer:

2x + 3y ≤ 15

To draw the graph follow the steps

1. Consider the function: 2x + 3y = 15

2. Find the y-intercept, the value of y, when x = 0:

x = 0 ⇒ 2*0 + 3y = 15 ⇒ 3y = 15 ⇒ y = 5

The point is (0, 5)

3. Find the x-intercept, the value of x, when y = 0:

y = 0 ⇒ 2x + 3*0 = 15 ⇒ 2x = 15 ⇒ x = 7.5

The point is (7.5, 0)

4. Note the inequality symbol ≤, which means less or equal, which includes all the points of the line. It means we draw a solid line connecting the points we have identified above.

5. Now, ignore all the numbers and only consider the sign of y and the inequality:

y ≤ k, is the simplest form

This tells we should make the region below the line shaded, which is the solution of the given inequality.

Step-by-step explanation:

Answer 2

Answer:

Given function:

• 2x + 3y ≤ 15

To draw the graph follow the steps

1. Consider the function: 2x + 3y = 15

2. Find the y-intercept, the value of y, when x = 0:

• x = 0 ⇒ 2*0 + 3y = 15 ⇒ 3y = 15 ⇒ y = 5
• The point is (0, 5)

3. Find the x-intercept, the value of x, when y = 0:

• y = 0 ⇒ 2x + 3*0 = 15 ⇒ 2x = 15 ⇒ x = 7.5
• The point is (7.5, 0)

4. Note the inequality symbol ≤, which means less or equal, which includes all the points of the line. It means we draw a solid line connecting the points we have identified above.

5. Now, ignore all the numbers and only consider the sign of y and the inequality:

• y ≤ k, is the simplest form

This tells we should make the region below the line shaded, which is the solution of the given inequality.

See attached