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Find the Function of a Graph

It’s important, when working with linear functions, to be able to find the equation of a linear function by reading a graph of the function.

It’s actually a lot easier than it sounds, as long as you remember that all linear functions graph as straight lines that are written as f(x) = ax + b, where a is the slope and b y-intercept (the constant term). Here are instructions for how to do it:


Finding the Equation of a Function from a Graph

Calculate the slope a, either by the formula for the slope, or by manually counting how much y increases or decreases by when you move x one place to the right.
Find the y intercept b by locating where the graph intersects the y-axis.
Insert the values into the expression f(x) = ax + b.

Example 1

Find the equation of the function from the graph.

A straight line going through (0, 16) and (4, 0)

Use the formula for the slope: a = 0 16 4 0 = 16 4 = 4

You can also find the answer graphically by moving along the x-axis one place to the right. You can see that the y-value goes from 16 to 12. That means it decreases by 16 12 = 4. Thus, the slope is 4.

Find the y-intercept, b, on the graph. From the drawing, you can see that the graph intersects the y-axis at y = 16.
Insert the values into the expression f(x) = ax + b.
You get f(x) = 4x + 16, the function of this graph.

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