Slope and 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

What is the slope formula?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is given by the formula: m = (y2 - y1) / (x2 - x1).

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 the y-value as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in a vertical line, where the x-value does not change, leading to division by zero in the slope formula.

Front

Calculate the slope between the points (2, 3) and (5, 7).

Back

m = (7 - 3) / (5 - 2) = 4 / 3.

Front

Calculate the slope between the points (1, 2) and (1, 5).

Back

The slope is undefined because the x-values are the same.

Front

If a line has a slope of 6, what does this mean in terms of rate of change?

Back

A slope of 6 means that for every 1 unit increase in x, the y-value increases by 6 units.

Front

What is the slope of a line that runs parallel to the x-axis?

Back

The slope of a line parallel to the x-axis is 0.