Rate of Change and Initial Value (Verbal/Equations)

Front

What is the initial value in a linear equation?

Back

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

Front

What does the rate of change represent in a linear function?

Back

The rate of change represents how much the dependent variable changes for each unit increase in the independent variable, often referred to as the slope.

Front

In the equation y = mx + b, what does 'b' represent?

Back

In the equation, 'b' represents the initial value or y-intercept, which is the value of y when x is 0.

Front

In the equation y = mx + b, what does 'm' represent?

Back

In the equation, 'm' represents the rate of change or slope, indicating how steep the line is.

Front

If a function has a rate of change of $0.60, what does this mean in a real-world context?

Back

It means that for every unit increase in the independent variable, the dependent variable increases by $0.60.

Front

What is the difference between initial value and rate of change?

Back

The initial value is the starting point of the function, while the rate of change indicates how the function increases or decreases.

Front

How do you find the initial value from a graph?

Back

The initial value can be found by identifying the point where the line crosses the y-axis.

Front

What is an example of a real-world situation that involves rate of change?

Back

An example is a taxi fare that increases by a certain amount per mile driven, where the rate of change is the fare per mile.

Front

If a waffle cone costs $1.85 and each scoop of ice cream costs $0.60, what is the total cost for 2 scoops?

Back

The total cost is $1.85 + (2 * $0.60) = $1.85 + $1.20 = $3.05.

Front

What does it mean if the rate of change is negative?

Back

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