Unit 4 Test Review

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 (>, <, ≥, ≤). It represents a region of the coordinate plane.

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 it mean for a system of inequalities to have no solution?

Back

A system of inequalities has no solution when the shaded regions of the inequalities do not overlap, meaning there is no point that satisfies all inequalities.

Front

What is the solution to a system of linear equations?

Back

The solution to a system of linear equations is the point (or points) where the lines intersect, representing the values of the variables that satisfy all equations.

Front

What does it mean if a system of equations has infinite solutions?

Back

A system of equations has infinite solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

How do you determine if a point satisfies a linear inequality?

Back

To determine if a point satisfies a linear inequality, substitute the x and y values of the point into the inequality. If the inequality holds true, the point satisfies 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. It represents the value of y when x is 0.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run). It indicates the direction of the line.

Front

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more inequalities that involve the same variables. The solution is the region where the shaded areas of the inequalities overlap.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.