Graphing Systems of Equations

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never intersect. They have the same slope.

Front

What does it mean if two lines have the same slope?

Back

If two lines have the same slope, they are parallel and will never intersect.

Front

What is the solution to a system of equations?

Back

The solution to a system of equations is the point where the graphs of the equations intersect.

Front

What does it mean if a system of equations has no solution?

Back

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

Front

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

Back

A system of equations has infinitely many solutions if the lines are the same, meaning they overlap completely.

Front

How can you determine if two lines are parallel from their equations?

Back

Two lines are parallel if they have the same slope in their slope-intercept form (y = mx + b).

Front

What is the slope-intercept form of a line?

Back

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

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis (x=0).

Front

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

Back

To find the solution graphically, plot both equations on the same graph and identify the point of intersection.

Front

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

Back

If two lines intersect at one point, the system of equations has one unique solution.