Finding Slope

Front

What is slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y (rise) over the change in x (run).

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 does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in 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, resulting in a downward trend.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, meaning there is no change in y as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero.

Front

Find the slope of the line through the points (2, 4) and (6, 8).

Back

The slope is m = (8 - 4) / (6 - 2) = 4 / 4 = 1.

Front

Find the slope of the line through the points (1, 2) and (3, 6).

Back

The slope is m = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the slope of the line represented by the equation y = -2x + 5?

Back

The slope is -2.

Front

If a line has a slope of 3, what does this mean?

Back

This means that for every 1 unit increase in x, the y-value increases by 3 units.