Slope from a Table

Front

What is the definition of slope?

Back

The slope is a measure of the steepness or incline of a line, 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, use the formula: Slope (m) = \frac{\text{Change in y}}{\text{Change in x}}.

Front

If the y-values increase by 8 and the x-values increase by 2, what is the slope?

Back

The slope is \frac{8}{2} = 4.

Front

What is the slope if the y-values decrease by 3 and the x-values increase by 1?

Back

The slope is \frac{-3}{1} = -3.

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

If a line has a slope of 5, what does this mean in terms of rise and run?

Back

A slope of 5 means that for every 1 unit increase in x (run), the y-value increases by 5 units (rise).

Front

How can you determine the slope from two points (x1, y1) and (x2, y2)?

Back

Use the formula: Slope (m) = \frac{y2 - y1}{x2 - x1}.