Key Features of 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 f(x) = 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

How do you calculate 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 y-intercept of a linear function?

Back

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

Front

How can you determine if a function is linear from its equation?

Back

A function is linear if it can be expressed in the form y = mx + b, where m and b are constants.

Front

What is the significance of the slope being positive, negative, or zero?

Back

A positive slope indicates that the function is increasing, a negative slope indicates that the function is decreasing, and a slope of zero indicates a horizontal line (no change in y).

Front

How do you interpret the slope of 1/2 in a real-world context?

Back

A slope of 1/2 means that for every 1 unit increase in x, the value of y increases by 1/2 unit.

Front

What is the formula for calculating the cost of renting a car based on distance driven?

Back

The cost can often be calculated using a linear equation of the form C = mx + b, where C is the total cost, m is the cost per mile, x is the number of miles driven, and b is the base fee.

Front

How can you use a linear function to model the growth of a plant over time?

Back

You can create a linear function where the independent variable represents time (days) and the dependent variable represents the height of the plant (cm).

Front

What does it mean if a linear function has a slope of 0?

Back

If a linear function has a slope of 0, it means that the function is constant and does not change regardless of the value of x.