rate of change and slope

Front

What is the definition of rate of change?

Back

The rate of change is a measure of how a quantity changes in relation to another quantity, often represented as the change in y over the change in x.

Front

What is the formula for calculating slope?

Back

Slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

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 2, what does this indicate about the line's steepness?

Back

A slope of 2 indicates that for every 1 unit increase in x, the value of y increases by 2 units, making the line steep.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x is 0, leading to division by zero.

Front

How do you find the slope between two points (3, 5) and (7, 9)?

Back

Using the formula: m = (9 - 5) / (7 - 3) = 4 / 4 = 1.

Front

True or False: The rate of change can be negative.

Back

True. A negative rate of change indicates that as one quantity increases, the other decreases.

Front

What is the relationship between rate of change and slope?

Back

Rate of change and slope are equivalent concepts; both describe how one quantity changes in relation to another.

Front

If the coordinates of two points are (1, 2) and (4, 5), what is the slope?

Back

The slope is (5 - 2) / (4 - 1) = 3 / 3 = 1.