Rate of Change

Front

What is the definition of Rate of Change?

Back

Rate of Change refers to how much a quantity changes in relation to another quantity. It is often represented as the slope of a line in a graph.

Front

What is the formula for calculating the slope (Rate of Change) between two points (x1, y1) and (x2, y2)?

Back

The formula is: \( m = \frac{{y2 - y1}}{{x2 - x1}} \)

Front

If the coordinates of two points are (3, 6) and (5, 6), what is the rate of change?

Back

0 (The y-values are the same, indicating no change in y.)

Front

What does a negative slope indicate about the rate of change?

Back

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

Front

What is the slope of a line that passes through the points (1, 2) and (4, 5)?

Back

The slope is \( m = \frac{{5 - 2}}{{4 - 1}} = 1 \)

Front

What is the relationship between the slope of a line and the steepness of the line?

Back

The greater the absolute value of the slope, the steeper the line. A slope of 0 indicates a horizontal line.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a line has a slope of -2, what does this mean in terms of rate of change?

Back

For every 1 unit increase in x, y decreases by 2 units.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope is 3.

Front

How do you interpret a slope of 0 in a real-world context?

Back

A slope of 0 indicates that there is no change in the dependent variable as the independent variable changes.