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Graphing Linear Inequalities on a Coordinate Plane, a la Shmoop

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

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

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

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

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…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]

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and posters of One Direction.

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

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

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

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

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

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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]…

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…then he can get the coveted wall side!

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

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

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1.

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

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

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The slope of the line is 2.

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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]

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1 unit to the right.

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

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

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

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

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negative 3.

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

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Yes! Success!

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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]

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the graph.

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