Slope/Average Rate of Change

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Front

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

Back

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

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

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 specific interval.

Front

How is average rate of change related to slope?

Back

The average rate of change over an interval is equivalent to the slope of the line connecting the endpoints of that interval on a graph.

Front

What is the formula for average rate of change between two points (x1, f(x1)) and (x2, f(x2))?

Back

Average Rate of Change = (f(x2) - f(x1)) / (x2 - x1)

Front

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

Back

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

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

What is the x-intercept of a line?

Back

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