Finding Slope from a Graph

Front

What is slope?

Back

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

Front

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

Back

Slope (m) is calculated using the formula: 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 slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change is 0, leading to division by zero.

Front

If a line rises 3 units for every 2 units it runs, what is the slope?

Back

The slope is 3/2.

Front

If a line falls 5 units for every 3 units it runs, what is the slope?

Back

The slope is -5/3.

Front

What is the slope of a line that goes through the points (1, 2) and (3, 6)?

Back

Using the formula, m = (6 - 2) / (3 - 1) = 4/2 = 2.

Front

What is the slope of a line that goes through the points (2, 3) and (2, 7)?

Back

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