4.4 - Graphing Linear Inequalities in Two Variables

Front

What is a linear inequality in two variables?

Back

A linear inequality in two variables is an inequality that can be written in the form ax + by <, >, ≤, or ≥ c, where a, b, and c are constants and x and y are variables.

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 values of x and y 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 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 of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine the slope from an equation in slope-intercept form?

Back

The slope is the coefficient of x in the equation y = mx + b.

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 identify the correct graph for a given inequality?

Back

To identify the correct graph, check the slope and y-intercept of the line, and ensure the shading corresponds to the inequality sign.

Front

What is the significance of the inequality sign in a linear inequality?

Back

The inequality sign indicates the relationship between the two sides of the inequality, determining which side of the line is shaded.

Front

How do you convert a linear inequality into slope-intercept form?

Back

To convert a linear inequality into slope-intercept form, isolate y on one side of the inequality.