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Given the graph of a line, we can write a linear function once we’ve extracted the slope and y–intercept of the graph. We will use the slope-intercept formula where m is the slope of the line and b is the y–values of the point where the line intersects the y–axis.
Ex1: Write the linear function for the graph
Step 1: Identify two points for which you can easily identify the coordinates.
Points A, B, and C are good example.
Step 2: Use the graph to determine the slope. Recall that slope is equal to rise over run . Count the number of units up or down and the number of units to the right. If counting up then slope is positive, if counting down then slope is negative.
Step 3: Identify the y–coordinate of the point where the line crosses the y–axis.
The line crosses the y–axis at (0, 1), therefore .
Step 4: Plug in the slope and y–intercept into the slope–intercept formula.
Ex 2: Write the linear function to the graph.
Step 1: Identify 2 points
(0, 4) & (3, 0)
Step 2: Count slope between points
Step 3: Identify y–intercept
b = 4
Step 4: Linear Function is:
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