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 the vertical direction (rise) divided by the change in the horizontal direction (run).

Front

How do you calculate the rate of change?

Back

Rate of change is calculated by dividing the change in the dependent variable by the change in the independent variable.

Front

What does a constant slope indicate?

Back

A constant slope indicates a linear relationship between two variables, meaning the rate of change is the same throughout.

Front

What is a non-linear relationship?

Back

A non-linear relationship is one where the rate of change varies, resulting in a curve rather than a straight line.

Front

If a line has a slope of 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in the x-direction, the y-value increases by 2 units.

Front

What is the slope of a line represented by the equation y = 3x + 1?

Back

The slope of the line is 3.

Front

How can you determine if a table of values represents a linear relationship?

Back

If the rate of change between the values is constant, the table represents a linear relationship.

Front

What is the formula for slope using two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a negative slope indicate?

Back

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

Front

What is the rate of change in the context of a real-world scenario?

Back

Rate of change can describe how quickly something is happening, such as speed (distance over time) or growth rate (population over time).