Graphing linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

Front

How do you graph a linear inequality in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the appropriate region based on 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 the set of points that satisfy the inequality.

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 can you determine which side of the line to shade when graphing a linear inequality?

Back

You can determine which side to shade by selecting a test point not on the line (commonly (0,0)) and substituting it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

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

Back

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

Front

How do you convert a linear equation to slope-intercept form?

Back

To convert a linear equation to slope-intercept form, solve for y in terms of x, isolating y on one side of the equation.

Front

What does the slope of a line represent in a linear inequality?

Back

The slope of a line represents the rate of change of y with respect to x, indicating how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept of a linear equation?

Back

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

Front

How do you identify the y-intercept from a linear equation in standard form?

Back

In standard form Ax + By = C, the y-intercept can be found by setting x = 0 and solving for y.