Match each inequality with its calculator graph. (Hint: Use the slope, y-intercept, and inequali

step 1 So for this problem, we have to match this inequality with one of the choices, A, B, C, or D. So

Match each inequality with its calculator graph. (Hint: Use...

Key Concepts

Shading or Region Selection

Shading is used in graphing inequalities to identify the set of all points that satisfy the inequality. Once the boundary line is drawn, the appropriate region (either above or below the line, depending on the inequality sign) is shaded to indicate where all the solution points lie. This visual representation is key for understanding the complete solution set of the inequality.

Boundary Line in Graphing Inequalities

When graphing linear inequalities, the boundary line represents the edge of the solution set. The style of this line—solid or dashed—indicates whether the boundary is included in the solution (inclusive) or not (exclusive). A solid line means the points on the line satisfy the inequality, while a dashed line indicates they do not.

Y-Intercept

The y-intercept is the point at which a line crosses the y-axis. This value is critical when plotting the line because it serves as a starting point, allowing you to accurately position the line relative to the coordinate axes. In linear equations and inequalities, knowing the y-intercept helps in sketching the overall line.

Slope

The slope is a measure of how steep a line is on a graph—it represents the rate of change between the dependent and independent variables. In the context of linear equations or inequalities, the slope helps determine the angle at which the boundary line is drawn, and it is essential for understanding the direction in which the graph rises or falls.

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