1A Graphing systems of 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 solution set of a system of linear inequalities represent?

Back

The solution set represents all the points that satisfy all inequalities in the system simultaneously.

Front

What is slope-intercept form?

Back

Slope-intercept form is a way of writing the equation of a line as y = mx + b, where m is the slope and b is the y-intercept.

Front

Convert -10x + 2y > 14 to slope-intercept form.

Back

y > 5x + 7.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it is a solution if the inequality is ≤ or ≥; otherwise, it is not a solution.

Front

How do you determine if a point is a solution to a linear inequality?

Back

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 difference between a dashed line and a solid line in graphing inequalities?

Back

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

Front

What is the first step in solving a system of inequalities by graphing?

Back

The first step is to graph each inequality on the same coordinate plane.

Front

What does the term 'feasible region' refer to in the context of linear inequalities?

Back

The feasible region is the area on the graph where all the shaded regions of the inequalities overlap, representing all possible solutions.