I don't get how you would know which way to shade the inequality when it's true or false.
For example the inequality 2x+3y> 12
When I solve it it's y>-2/3x+4
But when I graph the line how would I know which side to shade?
2x + 3y > 12.
Graph 2x + 3y = 12.
Use the following points:
(0,4), (6,0).
The graph should be a dotted line,
because the boundary line(graph) is not
a part of the solution. Therefore, the
points on the graph should not satisfy
the inequality. Let's test the 1st point:
2*0 + 3*4 > 12
12 > 12. Not true.
Imagine that the graph is a ramp and you are walking UP the ramp. The solution is to your right because the
arrow(>) points to the right. This is true only when the inequality is in the
standard form as given. Also, you must be walking UP the ramp.
The following points are to the rt. as
you walk UP the ramp and should,therefore,satisfy the inequality:
(0,5), (7,0).
2*0 + 3*5 > 12
15 > 12. True.
Test the 2nd point.
When graphing an inequality, such as in the example you provided (2x + 3y > 12), to determine which side of the line to shade, you can follow these steps:
1. Start by graphing the line as if it were an equation. In this case, the equation is 2x + 3y = 12. To graph this line, convert it into slope-intercept form (y = mx + b).
Rewrite the equation: 3y = -2x + 12
Divide both sides by 3: y = (-2/3)x + 4
2. The line y = (-2/3)x + 4 represents the boundary line for the inequality. Now you need to determine which side of the line to shade.
Choose a test point that is not on the line to determine which side to shade. An easy test point is (0, 0).
Substitute the test point into the original inequality:
2(0) + 3(0) > 12
0 > 12
3. Since the test point (0, 0) does not satisfy the original inequality (0 is not greater than 12), you can conclude that you need to shade the side of the line that does not contain the test point. In this case, you would shade the side of the line that is above the line.
So, when graphing the inequality 2x + 3y > 12, you would shade the region above the line y = (-2/3)x + 4.