Systems of Equations by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

How do you graph a linear equation?

Back

You plot points that satisfy the equation and then connect them with a straight line.

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

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept of a line?

Back

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

Front

How can you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

What is the graphical method for solving a system of equations?

Back

The graphical method involves plotting both equations on the same graph and identifying their intersection point.

Front

What does it mean if two lines intersect at one point?

Back

It means the system of equations has a unique solution.