Question

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

y > 3x + 10

y is less than negative 3 over 4 times x minus 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 (8, 10) included in the solution area for the system? Justify your answer mathematically

Answer 1

9514 1404 393

Answer:

A) The graph is the quadrant of the coordinate plane that lies between the two lines and to the left of the point (-2 14/15, 1 1/5)

B) no; it does not satisfy either inequality

Explanation:

A) The boundary line defined by the first inequality is a dashed line with a slope of 3 and a y-intercept of 10. Shading is above the line (and to its left).

The boundary line defined by the second inequality is a dashed line with a slope of -3/4 and a y-intercept of -1. Shading is below the line (and to its left).

The two lines cross at the 2nd-quadrant point (-2 14/15, 1 1/5). The solution area is the area between the crossing lines and to the left of that point. Neither that point nor any point on either line is part of the solution area.

The solution area is the doubly-shaded area in the attached graph.

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B) The first-quadrant point (8, 10) is not in the solution area, since the solution area is comprised of parts of quadrants 2 and 3 only.

We can see that (8, 10) will not satisfy either inequality:

10 > 3(8) +10 . . . . not true

10 < -3/4(8) -1 . . . . not true