Comparing 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 linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the dependent variable (y) changes for a unit change in the independent variable (x).

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the value of y when x is 0. It is 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 (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

If a linear function has a slope of 0, what does that indicate?

Back

A slope of 0 indicates that the function is constant; the value of y does not change regardless of the value of x.

Front

What does it mean for two linear functions to have the same rate of change?

Back

If two linear functions have the same rate of change, they have the same slope, meaning they increase or decrease at the same rate.

Front

How can you determine if a linear function is increasing or decreasing?

Back

A linear function is increasing if the slope is positive (m > 0) and decreasing if the slope is negative (m < 0).

Front

What is the significance of the rate of change in real-world applications?

Back

The rate of change helps to understand how one quantity changes in relation to another, which is crucial in fields like economics, physics, and engineering.

Front

What is a real-world example of a linear function?

Back

An example of a linear function is the cost of renting a car, where the total cost (y) can be represented as y = mx + b, with m being the cost per day and b being any fixed fees.