Determine rate of change from an equation

The rate of change in a linear relationship is the constant change in the dependent variable for each one-unit change in the independent variable, represented by the coefficient of $x$ when the equation is written as $y=mx+b$ , including negative or fractional coefficients. It determines the line’s direction and steepness and carries units, whereas $b$ represents the initial value or $y$ -intercept; nonlinear equations, variable rates, and more advanced equation forms are outside this scope.

Detailed Explanation: Determine rate of change from an equation

To find the rate of change, write the equation in the form

y=mx+b

The coefficient $m$ of $x$ is the rate of change. It tells how much $y$ changes when $x$ increases by 1. The number $b$ is the starting value, not the rate of change.

Example: Find the rate of change in

y=-\frac{1}{2}x+6

Step 1: Identify the coefficient of $x$ .

The coefficient of $x$ is

-\frac{1}{2}

So, the rate of change is

\boxed{-\frac{1}{2}}

Step 2: Interpret the rate.

For every increase of 1 in $x$ , the value of $y$ decreases by $\frac{1}{2}$ .

The negative sign means the relationship is decreasing. The $6$ is the initial value, or $y$ -intercept, not the rate of change.

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Determine rate of change from an equation

Detailed Explanation: Determine rate of change from an equation

Learn by doing: Determine rate of change from an equation

Practice with unlimited practice problems

Practice:

Slope - Find Equivalent - Slope Y Intercept Form to Decimal Slope