John R. answered • 02/20/13
John R: Math, Science, and History Teacher
Begin by solving each corresponding equation into slope-intercept form and graphing the line. The corresponding equation is the same as the inequality with the inequality replaced by an equal sign.
2y - x = -7
2y = x - 7
y = (1/2)x - 7/2
2y + 3x = 15
2y = -3x + 15
y = (-3/2)x + 15/2
The last two inequalities tell us that we are only looking in the first quadrant (x and y must be 0 or positive).
Using (0,0) as a test point, we can determine which side of the first two equations we are looking at:
2(0) - 0 > -7 2(0) + 3(0) < 15
0 - 0 > -7 0 + 0 < 15
0 > -7 0 < 15
Since both of these statements are true, the area between the two lines and the x and y-axis in the first
quadrant should be shaded as the answer.
Joseph J.
For each of the inequalities, if it includes equality (= or =) the edge (line) is part of the solution, and is indicated on a graph by a solid line. If it excludes equality (< or >), the edge is not part of the solution, and is indicated on a graph by a dashed line.
To check your work, you must verify two things:
One way to verify the lines is to check their intersection points. Each intersection point should satisfy both of the (original) corresponding equations. You don't need to check all of them; checking the intersection points on the edge of the solution set is sufficient. (An intersection point is the solution of the system of equations of the two intersecting lines.)
To check the directions, select any point within the common area, and it should make all of the original inequalities true.
02/20/13