#5.6 Graphing Linear Inequalities in Two Variables

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What is a linear inequality in two variables?

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

Front

What does the shaded region in a graph of a linear inequality represent?

Back

The shaded region represents all the solutions to the inequality. Points in this region satisfy the inequality, while points outside do not.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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A solid line indicates that points on the line are included in the solution (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

Front

How can you determine if a point is a solution to a linear inequality?

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To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the slope-intercept form of a linear equation?

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Front

How do you convert a linear equation to an inequality?

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To convert a linear equation to an inequality, replace the equality sign (=) with an inequality sign (<, >, ≤, or ≥) based on the context of the problem.

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Back

Front

What is the significance of the y-intercept in a linear inequality?

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The y-intercept is the point where the line crosses the y-axis. It helps in graphing the inequality and understanding the relationship between the variables.

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Back

This inequality indicates that y is less than or equal to the value of -x + 2, meaning y can take values on or below the line defined by the equation.