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

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid 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, indicating where the inequality holds true.

Front

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

Back

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

Front

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

Back

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

Front

How do you determine the slope of a line from its graph?

Back

The slope of a line is determined by the rise over run, which is the change in y divided by the change in x between two points on the line.

Front

What does it mean if a linear inequality has no solution?

Back

A linear inequality has no solution if the shaded regions do not overlap, indicating that there are no values that satisfy the inequality.

Front

What is the significance of the y-intercept in graphing linear inequalities?

Back

The y-intercept is the point where the line crosses the y-axis, and it helps to determine the starting point of the graph.

Front

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

Back

To check 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 standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.