145k views
1 vote
J

D
Which is the graph of linear inequality x - 2y 2-12?
10
8
201
$20
20
-10-B-BA -2e
t
10
10 x
49.
2+
-10-8-22-
4
6
the
2
6 8 10 x

User RasmusW
by
8.1k points

1 Answer

6 votes

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

User Ccallendar
by
8.4k points

Related questions