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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you calculate the slope between 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 y-intercept of a linear function?

Back

The y-intercept is the value of y when x = 0. It is the point where the line crosses the y-axis.

Front

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

Back

A linear function has a constant rate of change and graphs as a straight line, while a nonlinear function does not have a constant rate of change and can graph as curves or other shapes.

Front

What is the formula for a linear function?

Back

The formula for a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

If the slope of a line is positive, what does that indicate about the line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

If the slope of a line is negative, what does that indicate about the line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the initial value in the context of a linear function?

Back

The initial value refers to the y-intercept of the function, which is the starting value of y when x is 0.

Front

How can you identify a nonlinear function from a set of equations?

Back

A nonlinear function can be identified by its equation not being in the form y = mx + b, such as quadratic equations (e.g., y = ax^2 + bx + c) or circular equations.