Answer:
|
20 |
|
10 | shading
| |
| |
0 |_______|__________|__________
-10 -8 -2 10
| |
B- A
| |
-2 6
Explanation:
To graph the linear inequality x - 2y < 2 - 12, we can start by rearranging the inequality into slope-intercept form:
x - 2y < -10
-2y < -x - 10
y > 1/2 x + 5
The inequality y > 1/2 x + 5 represents a half-plane above the line y = 1/2 x + 5. The line has a y-intercept of 5 and a slope of 1/2. To graph this line, we can plot the y-intercept (0,5) and then use the slope to find additional points on the line. For example, we can move one unit to the right and two units up from the y-intercept to get the point (1,6), and then draw a line through both points.
Next, we need to shade the half-plane above the line to represent the inequality y > 1/2 x + 5. To do this, we can pick any point that is not on the line, such as the origin (0,0), and test whether it satisfies the inequality. Plugging in x = 0 and y = 0, we get:
0 > 1/2 (0) + 5
0 > 5
This is false, which means that the origin is not in the shaded region. Therefore, we need to shade the half-plane above the line.
|
20 |
|
10 | shading
| |
| |
0 |_______|__________|__________
-10 -8 -2 10
| |
B- A
| |
-2 6