Question

A graph of an inequality is shown. A graph of a dashed line passes through the points negative 6,negative 2 and 6,negative 6 with shading below the line. Explain if the point (6, –5) is part of the solution set shown on the graph.

Answer 1

The point (6, -5) is not part of the solution set shown on the attached graph of the inequality created with MS Excel

The steps used to evaluate the point (6, -6) can be presented as follows;

The points on the graph of the inequality are; (-6, -2), (6, -6)

The slope of the line of the graph is therefore; (-6 - (-2))/(6 - (-6)) = -1/3

The equation of the graph is therefore;

y - (-2) = (-1/3)·(x - (-6))

y = -x/3 - 2 - 2

y = -x/3 - 4

The shaded region of the graph is the region below the line, therefore, we get;

y < -x/3 - 4

When x = 6, we get;

-6/3 - 4 = -6

-6 < -5, or -5 > -6, therefore, the point (6, -5) is higher than the corresponding point on the line, which is; (6, -6). The point (6, -5) is in the region above the line of the inequality and is therefore not part of the solution set