Slope Basics

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

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate 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-coordinate increases, the y-coordinate decreases, 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, indicating that there is no vertical change as the x-coordinate changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines, where the x-coordinate remains constant while the y-coordinate changes, resulting in a division by zero.

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 is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation of a line y = mx + b.

Front

If a line has a slope of 5, what does this mean?

Back

A slope of 5 means that for every 1 unit increase in the x-direction, the y-value increases by 5 units.

Front

If a line has a slope of -3, what does this mean?

Back

A slope of -3 means that for every 1 unit increase in the x-direction, the y-value decreases by 3 units.

Front

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

Back

The slope of a perfectly horizontal line is 0.