One of them is a video that explains how to graph a linear inequality using slope-intercept form. Another one is a website that shows how to write linear inequalities in slope-intercept form from graphs. Here are the main steps to follow:
- Get your inequality into slope-intercept form (y=mx+b). You can use an equal sign or the given inequality symbol.
- Graph the line. If the inequality uses < or >, the line should be dotted. If the inequality uses ≤ or ≥, the line should be solid.
- Choose a test point on either side of the line and plug it into the inequality. If the inequality is true, shade that side of the line. If the inequality is false, shade the other side of the line.
For example, let's graph the inequality y < 2x - 3.
- The inequality is already in slope-intercept form, with m = 2 and b = -3.
- To graph the line, we can use the y-intercept (0, -3) and the slope 2/1 to find another point (1, -1). We connect these points with a dotted line because the inequality uses <.
- To choose a test point, we can use (0, 0), which is easy to plug in. We get 0 < 2(0) - 3, which simplifies to 0 < -3. This is false, so we shade the side of the line that does not contain (0, 0).
Here is a graph of the solution:
```
|y
|
| /
| / shaded region
| o/
| / |
|/ |
+---+---+--- x
```
I hope this helps you understand how to graph linear inequalities in slope-intercept form.