Question

1. Here is a graph of the equation 2y - x= 1. a. Are the points (0,5) and (–7,-3) solutions to the equation? Explain or show how you know. 2 8 6 N 6 8 b. Check if each of these points is a solution to the inequality 2y-x > 1: 2. 4 6 (0.2) (8,5 (-6,3) (-7,-3) do c. Shade the region that represents the solution set to the inequality 2y - x > 1. d. Are the points on the line included if the solution set? Explain how you know

Answer 1

a.

2y - x = 1

Replacing with the point (0, 1/2) into the equation, we get:

2(1/2) - (0) = 1

1 - 0 = 1

1 = 1

Then, (0, 1/2) is a solution of the equation.

Replacing with the point (-7, -3) into the equation, we get:

2(-3) - (-7) = 1

-6 + 7 = 1

1 = 1

Then, (-7, -3) is a solution of the equation.

b.

2y - x > 1

Replacing with the point (0, 2) into the inequality, we get:

2(2) - (0) > 1

4 - 0 > 1

4 > 1

Then, (0, 2) is a solution of the inequality.

Replacing with the point (8, 1/2) into the inequality, we get:

2(1/2) - (8) > 1

1 - 8 > 1

-7 < 1

Then, (8, 1/2) is not a solution of the inequality.

Replacing with the point (-6, 3) into the inequality, we get:

2(3) - (-6) > 1

6 + 6 > 1

12 > 1

Then, (-6, 3) is a solution of the inequality.

Replacing with the point (-7, -3) into the inequality, we get:

2(-3) - (-7) > 1

-6 + 7 > 1

1 = 1

Then, (-7, -3) is not a solution of the inequality.

c. The region that represents the solution set to the inequality 2y - x > 1 is:

d. The points on the line are not included in the solution set because a '>' is used. If the sign was '≥' then the line would be included