Characteristics of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in 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 the y-value with respect to the x-value. It indicates how steep the line is.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How do you find the x-intercept of a linear function?

Back

To find the x-intercept, set y = 0 in the equation of the line and solve for x.

Front

What is the difference between positive and negative slope?

Back

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

Front

What does a slope of zero indicate?

Back

A slope of zero indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where x remains constant while y changes.

Front

What is the domain of a linear function?

Back

The domain of a linear function is all real numbers, as x can take any value.

Front

What is the range of a linear function?

Back

The range of a linear function is also all real numbers, as y can take any value depending on the slope and y-intercept.

Front

How do you write the slope-intercept form of a linear equation?

Back

The slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.