Linear Functions

Front

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

Front

What is the slope in a linear function?

Back

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

Front

What is the y-intercept?

Back

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

Front

How do you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be expressed in the form f(x) = mx + b and its graph is a straight line.

Front

What is the general form of a linear equation?

Back

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

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions have varying rates of change and graph as curves.

Front

How can you identify a linear graph?

Back

A linear graph will always form a straight line when plotted on a Cartesian plane.

Front

What is the equation of a line with a slope of 2 and a y-intercept of -3?

Back

The equation of the line is y = 2x - 3.

Front

What does the term 'intercept' refer to in linear functions?

Back

Intercepts are points where the graph of the function crosses the axes. The x-intercept is where y=0, and the y-intercept is where x=0.