Comparing 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 linear function represent?

Back

The slope 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 a linear function?

Back

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

Front

How do you determine the rate of change from two points on a linear graph?

Back

The rate of change (slope) can be calculated using the formula (y2 - y1) / (x2 - x1) between two points (x1, y1) and (x2, y2).

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

What does a zero slope indicate about a linear function?

Back

A zero slope indicates that the function is constant, meaning y does not change as x changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where x does not change but y can take any value.

Front

How can you identify the slope from the equation of a linear function?

Back

In the equation y = mx + b, the slope is represented by the coefficient m.

Front

What is the significance of the initial sign-up fee in a gym membership cost equation?

Back

The initial sign-up fee is represented by the y-intercept in the equation, indicating the cost before any monthly fees are applied.