Finding Slope from 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 rise (change in y) over the run (change in x).

Front

How do you calculate the slope from a table of values?

Back

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

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, showing an upward trend.

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, showing a downward trend.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning there is no change in x (run = 0), which makes the slope calculation impossible.

Front

If the slope of a line is 3/1, what does this mean in terms of rise and run?

Back

A slope of 3/1 means that for every 1 unit you move to the right (run), the line rises 3 units (rise).

Front

What is the slope of a line that goes through the points (2, 3) and (5, 9)?

Back

The slope is (9 - 3) / (5 - 2) = 6 / 3 = 2.

Front

If a table shows the values (1, 2) and (4, 5), what is the slope?

Back

The slope is (5 - 2) / (4 - 1) = 3 / 3 = 1.

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is 0, indicating no change in y as x changes.

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.