Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shown as a shaded region on one side of a boundary line.

Front

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

Back

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

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you graph the inequality y > 2x + 1?

Back

Graph the line y = 2x + 1 with a dashed line, then shade above the line to represent y values greater than the line.

Front

What does the inequality y ≤ -3/4x + 3 indicate about the graph?

Back

It indicates that the graph includes the line y = -3/4x + 3 (solid line) and shades below the line.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, which helps in graphing the inequality.

Front

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

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the general process for graphing a linear inequality?

Back

1. Rewrite the inequality in slope-intercept form. 2. Graph the boundary line. 3. Determine if the line is solid or dashed. 4. Shade the appropriate region.