Slope

Front

What is the definition of slope?

Back

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

Front

What is the formula to calculate slope?

Back

The formula to calculate slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing an upward trend.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing a downward trend.

Front

What does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in a vertical line, where x remains constant and y changes, indicating an infinite steepness.

Front

How do you find the y-intercept of a line?

Back

The y-intercept is found by setting x = 0 in the equation of the line and solving for y.

Front

What is the average rate of change?

Back

The average rate of change is the change in the value of a quantity divided by the change in another quantity, often calculated over an interval.

Front

Calculate the slope of the line passing through (3, 4) and (7, 10).

Back

The slope is (10 - 4) / (7 - 3) = 6 / 4 = 3/2.

Front

Calculate the slope of the line passing through (1, 2) and (1, 5).

Back

The slope is undefined because the x-values are the same, indicating a vertical line.