Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It 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 (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x is 0, representing the point where the line crosses the y-axis.

Front

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

Back

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

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

What is the standard form of a linear equation?

Back

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

Front

How can you determine if a function is linear from a table of values?

Back

A function is linear if the rate of change (slope) between any two points is constant.

Front

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

Back

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

Front

What is the formula for the slope-intercept form of a linear equation?

Back

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