Linear Functions

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 f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

What is the y-intercept (b) in a linear function?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of f(x) when x = 0.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope indicates that the line rises as it moves from left to right, while a negative slope indicates that the line falls as it moves from left to right.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts. They 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. This means one line has a slope that is the negative reciprocal of the other.

Front

How can you determine if a function is linear from a table of values?

Back

A function is linear if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the graphical representation of a linear function?

Back

The graphical representation of a linear function is a straight line on a coordinate plane.