Answer:
Sure, I'd be happy to help!
To graph the inequality -9x + 3y ≥ 3, we can start by graphing the line -9x + 3y = 0.
First, let's find the slope of the line. To do this, we can use the formula:
Slope = (3y - 9x) / (3y + 9x)
Simplifying this formula, we get:
Slope = (3y - 9x) / (3y + 9x) = (3 - 9) / (3 + 9) = -6 / 12 = -1/2
So, the slope of the line is -1/2.
Next, we can find the y-intercept of the line by substituting y = 0 into the equation -9x + 3y = 0.
Doing this, we get:
-9x + 3(0) = 0
Simplifying, we get:
-9x = 0
So, the y-intercept of the line is 0.
Now that we have the slope and y-intercept, we can graph the line using the following steps:
1. Start at the y-intercept (0, 0).
2. Move up 1 unit to the right (to (1, 0)).
3. Move down 1 unit to the left (to (-1, 0)).
4. Draw a line connecting these three points.
Here's the graph of the line:
---
Now, we can graph the inequality -9x + 3y ≥ 3. To do this, we'll shade in all the points that satisfy the inequality.
First, let's find the points that satisfy the inequality. To do this, we can substitute y = 0 into the inequality and see which points work.
Substituting y = 0, we get:
-9x + 3(0) ≥ 3
Simplifying, we get:
-9x ≥ 3
So, all points on the line -9x + 3y = 0 satisfy the inequality.
Now, we can shade in all the points on the line that satisfy the inequality. Here's the graph of the inequality:
---
The shaded in points are all the points that satisfy the inequality -9x + 3y ≥ 3.
Explanation: