Slope from a Table

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

Front

How do you calculate slope from a table of values?

Back

To calculate slope from a table, use the formula: Slope (m) = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points from the table.

Front

If the points (2, 3) and (5, 9) are given, what is the slope?

Back

Slope = (9 - 3) / (5 - 2) = 6 / 3 = 2.

Front

What does a positive slope indicate?

Back

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

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 has a slope of 1/2, what does this mean?

Back

A slope of 1/2 means that for every 2 units you move horizontally to the right, you move 1 unit up vertically.

Front

What is the slope of the line represented by the points (1, 2) and (3, 4)?

Back

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

Front

How can you tell if a slope is steep?

Back

A slope is considered steep if the absolute value of the slope is greater than 1.