Linear Relationships Review

The rate of change is the ratio of the change in the y-value to the change in the x-value, often represented as the slope of the line.

The equation can be written in the form y = mx + b, where m is the rate of change (slope) and b is the y-intercept.

The slope represents the steepness of the line and the direction of the relationship between the variables. A positive slope indicates an increasing relationship, while a negative slope indicates a decreasing relationship.

To find the slope, calculate the change in y divided by the change in x (rise/run) between two points.

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

The slope is -5.

y = 100 - 30x, where y is the height and x is time in minutes.

A negative slope indicates that as one variable increases, the other variable decreases.

If the differences between the y-values divided by the differences between the x-values are constant, the relationship is linear.

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