Find the Slope from Tables

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is 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 a table of values?

Back

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

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, showing an upward trend.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, 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 the slope is 1, what does this mean?

Back

A slope of 1 means that for every unit increase in x, there is a corresponding unit increase in y, indicating a 45-degree angle.

Front

What is the slope of the line represented by the points (2, 3) and (4, 7)?

Back

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

Front

How do you interpret a slope of -3?

Back

A slope of -3 means that for every 1 unit increase in x, the y-value decreases by 3 units, indicating a steep downward trend.

Front

What is the slope of the line if the coordinates are (1, 2) and (1, 5)?

Back

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