Question

graph the inequality x+3y<9

Answer 1

To graph the inequality x + 3y < 9, we can start by graphing the related equation x + 3y = 9, which is the boundary line of the inequality.

1. Start by rewriting the equation in slope-intercept form:
3y = -x + 9
y = (-1/3)x + 3

2. Plot the y-intercept at (0, 3).

3. Find another point on the line by finding the x-intercept:
0 = (-1/3)x + 3
(-1/3)x = -3
x = 9
Hence, another point on the line is (9, 0).

4. Plot the x-intercept at (9, 0).

5. Using the two points, draw a straight line to connect them. This line represents the equation x + 3y = 9.

Now, let's determine which side of the line to shade to represent the solution to the inequality x + 3y < 9.

6. Start by choosing a test point not on the line. For simplicity, we can use the origin (0, 0).

7. Substitute the test point into the inequality:
(0) + 3(0) < 9
0 < 9
The inequality is true for the point (0, 0).

8. Shade the side of the line where the test point satisfies the inequality. In this case, shade the region below the line.

Finally, we have the graph of the inequality x + 3y < 9. The shaded region below the line represents the solution.