Use the slope-intercept method to graph each inequality. 2...

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Key Concepts

Slope-Intercept Form

This form expresses a linear equation in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. It is useful for graphing because it provides a clear and immediate way to plot the line by starting at b on the y-axis and moving according to the slope.

Graphing Linear Inequalities

Graphing a linear inequality involves first graphing the corresponding linear equation. The inequality sign then indicates which portion of the graph should be shaded. A strict inequality (using > or <) requires that the boundary line is drawn as a dashed line to indicate that points on the line are not included in the solution set, while a non-strict inequality (using ? or ?) uses a solid line.

Boundary and Region Shading

The process involves drawing the boundary line defined by the equality, then determining which side of the line satisfies the inequality. Typically, a test point not on the line is selected to see if it satisfies the inequality; if it does, the region containing the test point is shaded. This visually represents the solution set of the inequality.

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