Graphing Linear Systems Review

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x = 0.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, then use the slope to find another point. Draw a straight line through the points.

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the lines are parallel and never intersect.

Front

What does it mean for a system of equations to have infinite solutions?

Back

A system of equations has infinite solutions when the equations represent the same line, meaning they overlap completely.

Front

How do you find the solution to a system of equations graphically?

Back

To find the solution graphically, graph each equation on the same set of axes and identify the point(s) where the lines intersect.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or equal to the other.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality as a line, then shade the appropriate region that satisfies the inequality.