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 find the y-intercept of a linear equation?

Back

To find the y-intercept of a linear equation in the form y = mx + b, identify the value of b, which is the point where the line crosses the y-axis (0, b).

Front

What is the x-intercept of a linear function?

Back

The x-intercept is the point where the line crosses the x-axis. It can be found by setting y = 0 in the equation and solving for x.

Front

What does a positive slope indicate about a line?

Back

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

Front

What does a negative slope indicate about a line?

Back

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

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where x remains constant, indicating that there is no change in y as x changes.

Front

What is the formula to 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

How can you determine if a line is horizontal?

Back

A line is horizontal if its slope is 0, meaning there is no change in y as x changes.

Front

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

Back

The y-intercept indicates the value of y when x is 0, representing the starting point of the line on the y-axis.