Slope Intro

Front

What is slope?

Back

Slope is a measure of the steepness 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 is slope calculated?

Back

Slope (m) = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the line.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing an upward trend.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing a downward trend.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it involves division by zero (no horizontal change).

Front

What does 'rise over run' mean?

Back

'Rise over run' is a phrase used to describe how slope is calculated: the rise (vertical change) divided by the run (horizontal change).

Front

What is the relationship between slope and linear equations?

Back

In linear equations of the form y = mx + b, 'm' represents the slope, indicating the steepness and direction of the line.

Front

What is a linear relationship?

Back

A linear relationship is one where the change in one variable is proportional to the change in another variable, resulting in a straight line when graphed.

Front

What is a proportional relationship?

Back

A proportional relationship is a specific type of linear relationship that passes through the origin (0,0), meaning the ratio of y to x is constant.