2.6 - Systems of Inequalities

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 an inequality to slope-intercept form?

Back

To convert an inequality to slope-intercept form, isolate y on one side of the inequality, resulting in y < mx + b or y > mx + b.

Front

What does the symbol '≥' indicate in an inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

What does the symbol '<' indicate in an inequality?

Back

The symbol '<' indicates that the value on the left is less than the value on the right.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a solid line for '≥' or '≤' and a dashed line for '<' or '>'. Then shade the appropriate region based on the inequality.

Front

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

Back

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

Front

How do you determine the solution set for a system of inequalities?

Back

The solution set for a system of inequalities is the region where the shaded areas of all inequalities overlap on the graph.

Front

What is the difference between a solid line and a dashed line when 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

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

Back

The slope of a line represents the rate of change of y with respect to x, indicating how steep the line is.

Front

How can you identify the slope from an inequality in slope-intercept form?

Back

The slope can be identified as the coefficient of x in the slope-intercept form equation (y = mx + b).