Constant Rate of Change/Slope/Direct Variation

Front

What is the definition of a constant rate of change?

Back

A constant rate of change refers to a situation where the change in one quantity is consistent with the change in another quantity, often represented as a linear relationship.

Front

What does slope represent in a graph?

Back

Slope represents the rate of change between two variables, indicating how much one variable changes in relation to another.

Front

What is the formula for calculating slope?

Back

Slope (m) = (Change in y) / (Change in x) or m = (y2 - y1) / (x2 - x1).

Front

What does it mean if two quantities are proportional?

Back

Two quantities are proportional if they maintain a constant ratio, meaning as one quantity increases or decreases, the other does so at a consistent rate.

Front

How do you identify if a table of values represents a proportional relationship?

Back

A table represents a proportional relationship if the ratio of y to x is constant for all pairs of values.

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, expressed as y = kx, where k is a non-zero constant.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

How do you graph a slope of 2/3?

Back

To graph a slope of 2/3, rise 2 units up and run 3 units to the right from a point on the line.

Front

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

Back

The rate of change describes how one quantity changes in relation to another, such as speed (distance over time) or rainfall (cm per hour).

Front

If a line has a slope of -5/4, what does this indicate?

Back

A slope of -5/4 indicates that for every 4 units you move to the right, the line moves down 5 units, showing a negative relationship.