6.4 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

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shaded on one side of a boundary line.

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 do you find the rate of change between two points?

Back

The rate of change is found using the formula (y2 - y1) / (x2 - x1).

Front

What is the rate of change for the points (1, 2) and (3, 6)?

Back

The rate of change is (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

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

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

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 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 graph the inequality y < 2x + 3?

Back

Graph the line y = 2x + 3 with a dashed line, then shade below the line to represent all values of y that are less than 2x + 3.

Front

What is the solution set of the inequality x + 5 > 10?

Back

The solution set is x > 5.