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Graphing Linear Inequalities on a Coordinate Plane 6270 Views


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Description:

When graphing inequalities, you graph the line, shade the corresponding side, and plug in the point. The end!

Language:
English Language

Transcript

00:04

Graphing Linear Inequalities on a Coordinate Plane, a la Shmoop

00:08

Carson and Peter are roommates in a college dorm. [Carson and Peter smiling and waving to the camera]

00:10

It's their first day of school at S-I-T, Shmoop Institute of Technology…

00:15

… and they need to decide who gets which side of the room. [Carson and Peter deciding who gets which side of the dorm room]

00:19

One side of the room has a nice window sill and night stand…

00:22

…while the other side has a huge blank wall to hang up all those high school prom pictures [blank wall side of the dorm with old high school prom pictures hung up]

00:27

and posters of One Direction.

00:29

One problem is....they both want the blank wall side of the room.

00:33

Being the problem solvers they are, they decide to create a math problem out of their dilemma.

00:37

They first divide the room with the equation: y equals 2x minus 1. [Carson and Peters dorm room made into a coordinate plain graph]

00:42

Then, they write 6 pairs of coordinates on pieces of paper and put them in a hat.

00:48

Three coordinates are on one side of the line, and three coordinates are on the other.

00:52

If Carson chooses the pair of coordinates such that y is greater than 2x minus 1 [Carson thinking about picking the right pieces of paper out of the hat]…

00:57

…then he can get the coveted wall side!

01:00

Peter shakes the hat...and Carson pulls out a (-1,0).

01:04

Now they just have to figure out if he chose a point that satisfies y greater than 2x minus

01:09

1.

01:10

Let's start by graphing the line: y equals 2x minus 1. [y equals 2x minus 1 mapped on a coordinate plane graph]

01:14

The equation is in slope-intercept form, so we can plot -1 on the y-axis.

01:19

The slope of the line is 2.

01:21

We know that slope is rise over run, so we can rise 2 units on the y-axis, and run over [finger pointing to 2 on the y axis of the coordinate plane]

01:27

1 unit to the right.

01:29

The inequality is only greater than, and does not include greater than or equal to, so that

01:35

means we draw a dotted line, not a solid line. [a dotted line through the coordinate plane graph]

01:39

Now, let's check to see if (-1,0) fits the requirement.

01:43

We can substitute x equals -1 into the equation to get 2 times negative 1 minus 1, which equals

01:49

negative 3.

01:51

Is the given y-value of 0 greater than -3? [person picking a piece of paper with (-1, 0) out of a hat]

01:54

Yes! Success!

01:55

And because Carson feels like it, he decides to shade in his side of the room to complete [Carson painting his side of the room yellow]

02:00

the graph.

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