Compare Functions (2)

Front

What is the rate of change of a linear function?

Back

The rate of change of a linear function is the ratio of the change in the y-values to the change in the x-values, often represented as the slope (m) of the line.

Front

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

Back

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

Front

What is the initial value of a function?

Back

The initial value of a function is the value of the function when the independent variable (usually x) is zero, often represented as the y-intercept.

Front

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

Back

Two functions have the same rate of change if their slopes are equal, meaning they increase or decrease at the same rate.

Front

How can you compare the steepness of two linear functions?

Back

The steepness of a linear function is determined by its slope; a greater absolute value of the slope indicates a steeper line.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean if a function has a negative slope?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the function is decreasing.

Front

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

Back

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

Front

How do you determine which linear function has the greatest slope?

Back

To determine which linear function has the greatest slope, compare the slopes (m values) of each function; the function with the highest m value has the greatest slope.

Front

What does it mean for two functions to have different initial values?

Back

Two functions have different initial values if their y-intercepts are not equal, indicating they start at different points on the y-axis.