Question

Which statements are true about the linear inequality y > 3/4x – 2?

1. The slope of the line is -2
2. The graph of y>3/4x-2 is a dashed line
3.The area below the line is shaded
4. One solution to the inequality is (0,0)
5. The graph intercepts the y axis at (0,-2)

Answer 1

The slope of the line is .75, so 1. is false.

The graph is a dashed line AND the area above it shaded, so 2. is false (in and of itself)

The graph is the area shaded above the line not below it, so 3. is false.

0>.75(0)-2, 0>-2 so 4. is TRUE

The line is dashed and is not part of the solution to the inequality, so the point (0,-2) while on the line, is not part of the solution set and thus is not part of the graph, and does not intercept the graph, so 5. false. (the line intercepts the y axis at (0, -2) but the line itself is not part of the solution set and thus is not part of the graph)

So only statement 4. is true.