Linear Functions and Systems of Linear Equations

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line measures its steepness and direction. It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you find the slope between two points?

Back

To find the slope (m) between two points (x1, y1) and (x2, y2), use the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of 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.

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.

Front

How do you solve a system of linear equations?

Back

A system of linear equations can be solved using methods such as substitution, elimination, or graphing.

Front

What is the elimination method?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What is the substitution method?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is a solution to a system of equations?

Back

A solution to a system of equations is a set of values for the variables that makes all equations in the system true.