Calculating Slope

Front

What is slope?

Back

Slope is a measure of the steepness of a line, calculated as the change in vertical distance (rise) divided by the change in horizontal distance (run).

Front

How do you calculate the slope of a line given 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 vertical line?

Back

The slope of a vertical line is undefined because the run (change in x) is zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because there is no change in y (rise) as x changes.

Front

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

Back

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

Front

What is the slope of the line represented by the equation y = 4x + 1?

Back

The slope of the line is 4.

Front

How can you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line, calculating the rise over run between them.

Front

What is the slope of the line that passes through the points (2, 3) and (5, 11)?

Back

Slope = (11 - 3) / (5 - 2) = 8 / 3.