Slope - Tables

Front

What is the definition of slope in mathematics?

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 between 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 has a slope of 2, what does this mean in terms of rise and run?

Back

A slope of 2 means that for every 1 unit of horizontal change (run), the vertical change (rise) is 2 units.

Front

Given the points (1, 2) and (3, 6), what is the slope?

Back

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

Front

What is the slope of the line represented by the table of values: (0, 0), (1, 3), (2, 6)?

Back

Slope = (6 - 0) / (2 - 0) = 6 / 2 = 3.

Front

If a table shows a constant rate of change, what does this imply about the slope?

Back

It implies that the slope is constant, meaning the relationship between the variables is linear.