I need help with this problems graph inequalities 3x-4y<12.
To graph the inequality 3x - 4y < 12, we can follow these steps:
Step 1: Start by graphing the related equation, 3x - 4y = 12.
To do this, we can rewrite the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Rearranging the equation, we have:
-4y = -3x + 12
Dividing through by -4, we get:
y = (3/4)x - 3
Now, we can plot the y-intercept, which is at (0, -3), and use the slope to find additional points. The slope is 3/4, which means that for every 4 units of horizontal change (x), there is 3 units of vertical change (y). So, starting from the y-intercept, we can move 4 units to the right and 3 units up to locate another point. Connecting these two points gives us a line.
Step 2: Determine the region to shade.
To determine which side of the line to shade, we need to choose a test point not on the line. A convenient choice is the origin (0, 0). Substitute the x and y values of the origin into the original inequality: 3(0) - 4(0) < 12. Simplify to 0 < 12, which is true.
Since the origin satisfies the inequality, we shade the region that contains the origin. This will be the region below the line.
Step 3: Graph the inequality.
Now, we can graph the inequality by shading the appropriate region below the line.
Here's the graphical representation of the inequality 3x - 4y < 12:
```
|
| shaded region
| below the line
|
----|------------------------------------
|
```