Finding Slope from a Table & Graph

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented 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 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-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 that the line is horizontal and there is no vertical change as the x-values change.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning there is no horizontal change as the x-values change.

Front

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

Back

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

Front

If a line passes through the points (1, 2) and (1, 5), what is the slope?

Back

Slope is undefined because the x-values are the same, indicating a vertical line.

Front

What is the slope of a line that runs parallel to the x-axis?

Back

The slope is zero.

Front

What is the slope of a line that runs parallel to the y-axis?

Back

The slope is undefined.