Slope from Graphs

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 (rise) to the horizontal change (run) between two points on the line.

Front

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

Back

Slope (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.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change.

Front

If a line rises 3 units for every 4 units it runs, what is the slope?

Back

The slope is 3/4.

Front

If a line falls 2 units for every 5 units it runs, what is the slope?

Back

The slope is -2/5.

Front

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

Back

Slope = (6 - 2) / (3 - 1) = 4/2 = 2.

Front

What is the slope of a line that goes through the points (2, 3) and (2, 5)?

Back

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