Rate of Change and Initial Value (Verbal/Equations)

Front

What is the definition of rate of change?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity, often represented as the slope in a linear equation.

Front

In the context of a linear equation, what does the slope represent?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

Front

What is the initial value in a linear equation?

Back

The initial value is the y-intercept of the equation, representing the value of the dependent variable when the independent variable is zero.

Front

How do you identify the rate of change from an equation in the form y = mx + b?

Back

The rate of change is represented by 'm', which is the coefficient of 'x'.

Front

What is the initial value in the equation y = 3x + 5?

Back

The initial value is 5, which is the y-intercept.

Front

If a function has a rate of change of 4, what does this imply about the relationship between the variables?

Back

It implies that for every 1 unit increase in the independent variable, the dependent variable increases by 4 units.

Front

In the equation y = -2x + 10, what is the rate of change?

Back

The rate of change is -2.

Front

What does a positive rate of change indicate about a function?

Back

A positive rate of change indicates that as the independent variable increases, the dependent variable also increases.

Front

What does a negative rate of change indicate about a function?

Back

A negative rate of change indicates that as the independent variable increases, the dependent variable decreases.

Front

How can you find the initial value from a word problem involving a fixed cost?

Back

The initial value is the fixed cost mentioned in the problem, which is the cost incurred when no variable costs are added.