Finding Slope from a Graph or Two Points

Front

What is slope?

Back

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

Front

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

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does it mean if the slope is positive?

Back

A positive slope indicates that as you move from left to right on the graph, the line rises. This means that the y-value increases as the x-value increases.

Front

What does it mean if the slope is negative?

Back

A negative slope indicates that as you move from left to right on the graph, the line falls. This means that the y-value decreases as the x-value increases.

Front

What does it mean if the slope is zero?

Back

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

Front

What does it mean if the slope is undefined?

Back

An undefined slope occurs when a line is vertical, meaning that the x-value does not change while the y-value does.

Front

If a line passes through the points (2, 3) and (5, 7), what is the slope?

Back

Using the formula m = (y2 - y1) / (x2 - x1), the slope is m = (7 - 3) / (5 - 2) = 4 / 3.

Front

If a line passes through the points (1, 2) and (1, 5), what is the slope?

Back

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

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.