Find Slope from a Table, Graph, and Two Points

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the ratio of the rise (change in y) to the run (change in x).

Front

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

Back

The slope (m) can be calculated using the formula: m = (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, 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 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 with a vertical line, where the change in x is zero, leading to division by zero in the slope formula.

Front

How can you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, determine the rise and run between them, and use the formula m = rise/run.

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

Using the formula m = (y2 - y1) / (x2 - x1), the slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined because the run (change in x) is zero.

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is zero because there is no change in y as x changes.