Slope (from a graph)

Front

What is the definition of slope?

Back

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 of a line given two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, 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-value increases, the y-value decreases, 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 vertical change as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in a vertical line where the x-value does not change, resulting in a division by zero when calculating slope.

Front

Find the slope of the line that passes through the points (2, 3) and (5, 7).

Back

Slope = (7 - 3) / (5 - 2) = 4/3.

Front

Find the slope of the line that passes through the points (1, 2) and (1, 5).

Back

Slope is undefined because the x-values are the same.

Front

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

Back

The slope is 0.

Front

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

Back

The slope is undefined.