Cabins: Slope and Rate of Change

Front

What is the definition of slope?

Back

Slope is a measure of the steepness of a line, calculated as the change in y (rise) divided by the change in x (run).

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it goes straight up and down.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the formula for the slope-intercept form of a line?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does 'm' represent in the equation y = mx + b?

Back

In the equation, 'm' represents the slope of the line.

Front

What are the x- and y-intercepts of a line?

Back

The x-intercept is the point where the line crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0).

Front

What is the rate of change in a linear function?

Back

The rate of change is the same as the slope, representing how much y changes for a unit change in x.

Front

What does 'rise over run' mean in the context of slope?

Back

'Rise over run' refers to the vertical change (rise) divided by the horizontal change (run) between two points on a line.

Front

If a line has a slope of -1, what does this indicate about its direction?

Back

A slope of -1 indicates that the line descends from left to right.

Front

What is the significance of a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.