Question

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:

y > 5x + 5
y is greater than negative 1 over 2 times x plus 1

Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)
Part B: Is the point (−2, 5) included in the solution area for the system? Justify your answer mathematically. (4 points)

Answer 1

Step-by-step explanation:

Part A.

The boundary lines of both inequalities will be dashed, because neither includes the "or equal to" case.

The first inequality solution area is bounded by a line with slope +5 and y-intercept +5. The solution area is above the line (y is greater than ...). Since the line rises steeply, the solution area looks to be to the left of the line. (It is shaded red on the attached graph.)

The second inequality solution area is bounded by a line with slope -1/2 and y-intercept +1. The solution area for this inequality is also above the line.

The solution area is where the two solution spaces overlap, in the quadrant to the upper left of the point where the lines intersect.

___

Part B.

The graph shows the point (-2, 5) to be in the solution space.

We can show this point satisfies both inequalities.

• 5 > 5(-2)+5 ⇒ 5 > -5 . . . true
• 5 > (-1/2)(-2) +1 ⇒ 5 > 2 . . . true