Question

Graph the inequality using intercepts.

5x - 10y ≥ 30

Answer 1

5x - 10y = 30

Divide both sides by 5:
x - 2y = 6

Set y = 0, then solve for x
x - 5(0) = 6
x = 6

So the first intercept is (6,0)

Set x = 0, then solve for y:
0 - 2y = 6
-6 = 2y
-6/2 = y
-3 = y

So the other intercept is (0, -3)

Answer 2

After plotting the points, draw a line through it. Then test which region using the point (0,0).

Answer 3

okay :) so would the line be dotted or solid?

Answer 4

Of course it will be solid because when you have \(\ge\) or \(\le\) it will be a solid line. If it were just \(>\) or \(<\) it would be dotted

Answer 5

thanks a lot :)

Answer 6

The key thing here though is testing out which region to shade.

Answer 7

Using (0,0)

Answer 8

There are two ways to do it actually.

Answer 9

You could either test out the region using (0,0) or you can isolate y

Answer 10

Suppose you test (0,0):

5(0) - 10(0) ≥ 30

0 ≥ 30 False

So the shaded region must exist below the line

Answer 11

If you isolated y, you would get:


\(y \le \dfrac{x - 6}{2}\)

Then because y is LESS THAN or equal to the expression, then that means the shaded region is below the line

Answer 12

oh okay :) i get it

Answer 13

Here's what it looks like:

https://www.desmos.com/calculator/og9hqiulzb

Answer 14

Notice that (0,0) is not in the shaded region because when we tested it, we got a false result.

Answer 15

The approach to doing these is always the same:

1. Plot the line (or dotted line)
2. Test which region to shade using (0,0) (or just isolate y)
3. Then shade the proper region