Finding Slope from Two Points or a Table

Front

What is the formula to find the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = \frac{y2 - y1}{x2 - x1}.

Front

What does a positive slope indicate about a line on a graph?

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 on a graph?

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 does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that there is no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning there is no change in x as y changes.

Front

Find the slope of the points (2, 3) and (5, 11).

Back

m = \frac{11 - 3}{5 - 2} = \frac{8}{3}.

Front

Find the slope of the points (4, 2) and (4, 6).

Back

The slope is undefined because the x-values are the same (4).

Front

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

Back

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

Front

What is the slope of the line represented by the table if the y-values increase by 2 and the x-values increase by 1?

Back

The slope is \frac{2}{1} = 2.

Front

Find the slope from the table: x: 1, 2, 3; y: 2, 4, 6.

Back

The slope is \frac{6 - 2}{3 - 1} = \frac{4}{2} = 2.