Slope Basics

Front

What is the definition of slope?

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 between 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 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 vertical lines where the x-value does not change, leading to a division by zero in the slope formula.

Front

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

Back

The slope is (11 - 3) / (5 - 2) = 8 / 3.

Front

Find the slope of the line through the points (0, 6) and (7, 6).

Back

The slope is (6 - 6) / (7 - 0) = 0, indicating a horizontal line.

Front

Find the slope of the line through the points (3, 18) and (0, 18).

Back

The slope is (18 - 18) / (3 - 0) = 0, indicating a horizontal line.

Front

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

Back

The slope is undefined, indicating a vertical line.