5.2 Graphing Systems

Front

What are parallel lines?

Back

Parallel lines are lines in a plane that never intersect and 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 two equations represent the same line.

Front

How can you determine if an ordered pair is a solution to a system of equations?

Back

Plug the x-value into both equations and check if the resulting y-values are equal.

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 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 slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to intersect?

Back

Two lines intersect if they cross each other at a single point, which is the solution to the system.