Definition: A linear function is a function that has a constant rate of change and can be represented by the equation y = mx + b, where m and b are constants.

A constant rate of change means that for every change in x, there is the same change in y every time. Gasoline has a set price; this means each gallon costs a specific amount. Each gallon you get will add that amount to the total; this is a constant rate of change.

Introduction: Rate of Change The rate of change tells us how one quantity changes as the other changes. For a linear function, the rate of change is represented by the parameter m in the slope-intercept form for a line: y=mx+b, and is visible in a table or on a graph.

The rate of change is a ratio that compares the change in values of the y variables to the change in values of the x variables. If the rate of change is constant and linear, the rate of change is the slope of the line. The slope of a line may be positive, negative, zero, or undefined.

To find the average rate of change, we divide the change in the output value by the change in the input value.

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1 Answer. The average rate of change gives the slope of a secant line, but the instantaneous rate of change (the derivative) gives the slope of a tangent line. Also note that the average rate of change approximates the instantaneous rate of change over very short intervals.

Rates of change can be positive or negative. This corresponds to an increase or decrease in the y -value between the two data points.

The average rate of reaction is an average rate, obtained by taking the change in concentration over a time period. For example: -0.3 M / 15 minutes. The rate at which chemical substances react varies greatly. Usually, a reaction rate involves the change in the concentration of a substance over a given period of time.

However, it’s easier to use a handy formula: rate equals distance divided by time: r = d/t. Actually, this formula comes directly from the proportion calculation — it’s just that one multiplication step has already been done for you, so it’s a shortcut to learn the formula and use it.

Plan The average rate is given by the change in concentration, ∆[A], divided by the change in time, ∆t. Because A is a reactant, a minus sign is used in the calculation to make the rate a positive quantity.