Linear Functions

Front

What is the definition of a linear function?

Back

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

Front

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

Back

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

Front

What is the slope of the line represented by the equation y = 4x + 1?

Back

The slope of the line is 4.

Front

What is the y-intercept in the equation y = 3x - 5?

Back

The y-intercept is -5, which is the point where the line crosses the y-axis (0, -5).

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value).

Front

Identify whether the following set of points is a function: {(-1, 9), (0, 2), (-1, 3)}.

Back

This set of points is NOT a function because the input -1 corresponds to two different outputs (9 and 3).

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

How can you determine if a graph represents a linear function?

Back

A graph represents a linear function if it forms a straight line.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the value of y when x is 0.

Front

What is the difference between a linear function and a nonlinear function?

Back

A linear function has a constant rate of change and can be represented by a straight line, while a nonlinear function does not have a constant rate of change and can be represented by curves.