Slope from a Table

Front

What is the definition of 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 the slope from a table of values?

Back

To calculate the 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 coordinates of two points are (2, 3) and (4, 7), what is the slope?

Back

Slope = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, 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-values increase, the y-values decrease, 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

Given the points (1, 2) and (3, 6), find the slope.

Back

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

Front

If the slope of a line is -3, what does this tell you about the line's direction?

Back

A slope of -3 indicates that the line falls steeply from left to right.

Front

What is the slope of the line represented by the equation y = 2x + 1?

Back

The slope is 2, which means for every 1 unit increase in x, y increases by 2 units.