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 consistent?

Back

A system of equations is consistent if there is at least one solution that satisfies all equations in the system.

Front

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

Back

A system of equations is inconsistent if there are no solutions that satisfy all equations in the system.

Front

What is a dependent system of equations?

Back

A dependent system of equations has infinitely many solutions because the equations represent the same line.

Front

What is an independent system of equations?

Back

An independent system of equations has exactly one solution, where the lines intersect at a single point.

Front

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

Back

To find the solution graphically, plot the equations on a 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

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, meaning they have no solutions.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.