Graph the inequality.
x+3y>9
To graph the inequality x + 3y > 9, we first graph the line x + 3y = 9, and then shade the region above the line.
1. Graph the line x + 3y = 9:
To graph the line, we need to find its x-intercept and y-intercept, and then connect them with a straight line.
x-intercept: Set y = 0 and solve for x:
x + 3(0) = 9
x = 9
The x-intercept is (9, 0).
y-intercept: Set x = 0 and solve for y:
0 + 3y = 9
3y = 9
y = 3
The y-intercept is (0, 3).
Now draw a straight line passing through the points (9, 0) and (0, 3).
2. Shade the region above the line:
Since the inequality is x + 3y > 9, we need to shade the region above the line. This can be done by choosing a test point not on the line and checking whether it satisfies the inequality.
Let's choose the test point (0, 0).
Substituting x = 0 and y = 0 into the inequality:
0 + 3(0) > 9
0 > 9
Since 0 is not greater than 9, the test point (0, 0) does not satisfy the inequality.
As a result, we shade the region above the line.
The graph of the inequality x + 3y > 9 is a region above the line x + 3y = 9.