Solve and Graph 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 solid line (for ≥ or ≤) or a dashed line (for > or <). Then, shade the region that satisfies the inequality.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the graph of the equation crosses the y-axis, indicating the value of y when x is 0.

Front

Identify the y-intercept of the function: y = -3x.

Back

0

Front

What is the slope of the line represented by the equation y = mx + b?

Back

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

Front

What does it mean if a linear inequality has no solution?

Back

A linear inequality has no solution if the shaded regions do not overlap, meaning there are no values of x and y 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 check if a point is a solution to a linear inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

What does the term 'solution set' refer to in the context of linear inequalities?

Back

The solution set is the set of all points (x, y) that satisfy the linear inequality.