rate of change and slope

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Front

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

Back

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

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, 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-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a line passes through the points (1, 2) and (3, 6), what is the slope?

Back

Slope (m) = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the formula for rate of change?

Back

Rate of change = (y2 - y1) / (x2 - x1)

Front

If the rate of change is 3, what does this mean in terms of y and x?

Back

For every 1 unit increase in x, y increases by 3 units.

Front

Find the slope of the line that passes through the points (2, 4) and (6, 12).

Back

Slope (m) = (12 - 4) / (6 - 2) = 8 / 4 = 2.