Graphing Linear Inequalites

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 equation?

Back

The slope of a line can be determined from its equation in slope-intercept form (y = mx + b) as the coefficient m.

Front

What does the y-intercept represent in a graph?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

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

Back

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 significance of the boundary line in a linear inequality graph?

Back

The boundary line separates the graph into two regions: one that satisfies the inequality and one that does not.

Front

What are the four types of linear inequalities?

Back

The four types of linear inequalities are: 1) >, 2) <, 3) ≥, 4) ≤.