Linear Inequalities in two Variables Test #1

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In this section, we review how to graph a linear inequality in two variables. A linear inequality in two variables is of the form:
ax + by < c, where a, b, and c are real numbers, a and b are not both zero, and < could be: >, ≥, or ≤. To graph a linear
inequality in two variables, we solve the inequality for y. We then replace the inequality symbol with an equality symbol and graph the
resulting equation. This gives us our boundary line. The boundary line separates the solution region from the non-solution region.
The boundary line is dashed for a strict inequality and solid for a non-strict inequality. If our inequality is strict, the boundary
line is not part of the solution. Therefore a dashed line shows this line is excluded from the solution region. If the inequality is
non-strict, we draw a solid line to show the line is included. Once the boundary line is drawn, we shade below the line for a less
than and above the line for a greater than. Note this only works when we have solved the inequality for y. If we don’t solve the
inequality for y, we use a test point. The test point method tells us to choose a point on either side of the line. If that point
works as a solution to the inequality, the test point lies in the solution region and that region should be shaded. If the point
does not work, the test point lies in the non-solution region and we must shade the other region.

Linear Inequalities in two Variables Resources:

Videos:

Khan Academy - Video
Khan Academy - Video
Virtual Nerd - Video
Text Lessons:

Math Planet - Text Lesson
Varsity Tutors - Text Lesson
Purple Math - Text Lesson
Worksheets:

Kuta - Worksheet
Khan Academy - Worksheet
Khan Academy - Practice
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