Graphing Linear Systems

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 it mean for a system of equations to be independent?

Back

A system of equations is independent if it has exactly one solution, meaning the lines intersect at one point.

Front

What does it mean for a system of equations to be dependent?

Back

A system of equations is dependent if it has infinitely many solutions, meaning the equations represent the same line.

Front

What does it mean for a system of equations to be inconsistent?

Back

A system of equations is inconsistent if it has no solutions, meaning the lines are parallel and never intersect.

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 where the lines intersect.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

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 representation of the equation y = 2x + 3?

Back

The graph is a straight line with a slope of 2 and a y-intercept at (0, 3).