Slope and Slope Formula

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is 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 using two points (x1, y1) and (x2, y2)?

Back

The slope (m) is 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 you move from left to right along the line, the line rises. This means that the y-values increase as the x-values increase.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as you move from left to right along the line, the line falls. This means that the y-values decrease as the x-values increase.

Front

What does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating that there is no vertical change as the x-values change.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines, where the x-values are constant, leading to a division by zero in the slope formula.

Front

Find the slope of the line that goes through the points (2, 3) and (4, 7).

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

Find the slope of the line that goes through the points (−1,−2) and (−3,−4).

Back

The slope is m = (−4 - (−2)) / (−3 - (−1)) = (−4 + 2) / (−3 + 1) = −2 / −2 = 1.

Front

Find the slope of the line that goes through the points (−11,−5) and (1,−12).

Back

The slope is m = (−12 - (−5)) / (1 - (−11)) = (−12 + 5) / (1 + 11) = −7 / 12.

Front

What is the slope of a line that is perfectly vertical?

Back

The slope of a perfectly vertical line is undefined.