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  • Caroline Schreier

Linear Functions: How to write an equation given the graph

Being able to write an equation given the graph is an important skill which can also be applied to other types of functions later on.


Let's look at the example below.


To write a linear equation, you must find the value of m and b.

Since b is the y-intercept, or the point on the graph where x = 0, it can be found by going to x=0 and looking to see what the y-value is. On the graph above, the y-intercept is (0,4), so

b=4.

Since m is the rate of change, it can be found by determining the change between two points.

Step 1: Choose two defined points (it's easiest if they're close together).


Step 2: Count how many units vertically, and how many units to the side, it takes to get to the next point.


Step 3: Divide the number of vertical units by the number of horizontal units. In this case,

2/1 = 2, so m = 2

Now that you have determined the value for each variable, you can plug them into the equation: y = mx + b .

So, the final equation for this graph is: y = 2x + 4.


Now try some practice problems on your own:

1)













2)


















3)
















Answers:

1) Equation: y = .5x+3

Explanation: In this equation, you can see that for every 1 unit you go up, you must go right 2 units to reach the next defined point. Since 1 divided by to is .5 (or 1/2), m=.5 . For the y-intercept (b), you can see that when x = 0, y = 3 so the y-intercept is (0,3).

2) Equation: y = -2x+1

Explanation: In this equation, you can see that for every 2 units up, you must go left one unit to reach the next defined point (or for every 2 units down, you must go 1 unit right). Since 2 divided by -1 (or -2 divided by 1) is -2, m=-2. For the y-intercept (b), you can see that when x=0, y=1 so the y-intercept is (0,1).

3) Equation: y = -x - 3

Explanation: In this equation, you can see that for every 1 unit up, you must go 1 unit to the left (or for every 1 unit down, you must go 1 unit right). Since -1 divided by 1 is -1, m = -1. For the y-intercept (b), you can see that when x = 0, y = -3.


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