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 (such as <, >, ≤, or ≥).

Front

What does it mean if a line is dotted in a graph of a linear inequality?

Back

A dotted line indicates that the points on the line are not included in the solution set of the inequality.

Front

What does it mean if a line is solid in a graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set of the inequality.

Front

How do you determine 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 difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' represents a region not including the line, while 'y ≤ mx + b' includes the line.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be equal to or greater than the expression.

Front

How do you graph the inequality y < 2x + 3?

Back

1. Graph the line y = 2x + 3 with a dotted line. 2. Shade below the line to represent all points where y is less than the line.

Front

What is the solution set of the inequality 5x + y ≤ -1?

Back

The solution set includes all points (x, y) that satisfy the inequality, represented by the shaded region below the line 5x + y = -1.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you identify the y-intercept from the equation y = -2/5x + 1?

Back

The y-intercept is the value of y when x = 0, which is 1 in this case.