Comparing 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 of a linear function represent?

Back

The slope represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

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

Back

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

Front

What is the y-intercept in 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

What is the rate of change in a real-world context?

Back

The rate of change describes how one quantity changes in relation to another, often expressed as a cost per unit, such as dollars per hour.

Front

How can you compare the rates of change of two linear functions?

Back

You can compare the slopes of the functions. The function with the greater slope has a higher rate of change.

Front

What is the equation of a line with a slope of 2 and a y-intercept of -3?

Back

The equation is y = 2x - 3.

Front

If a function has a negative slope, what does that indicate?

Back

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

Front

What is the significance of a slope of zero?

Back

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

Front

How do you determine if two linear functions are parallel?

Back

Two linear functions are parallel if they have the same slope but different y-intercepts.