Slope/Average Rate of Change

Front

What is the formula to calculate the slope of a line?

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

How do you interpret the slope of a line?

Back

The slope represents the rate of change of y with respect to x; it indicates how much y changes for a unit change in x.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases.

Front

What is the average rate of change?

Back

The average rate of change is the change in the value of a function divided by the change in the input value over a specified interval.

Front

If a line passes through points (1, 3) and (4, 9), what is the slope?

Back

Slope = (9 - 3) / (4 - 1) = 6 / 3 = 2.

Front

What is the average rate of change of a function f(x) from x = a to x = b?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a).

Front

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

Back

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

Front

How can you determine the interval with the greatest average speed from a graph?

Back

Look for the steepest slope on the graph, as it indicates the greatest change in distance over time.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.