Suppose that we have the graph shown below.
Using this example graph, we will illustrate two methods to find the equation of a line given its graph.
Finding the Equation Using the Point-Slope Form
One way is to use the .
y-y_1 = m (x-x_1)
Here m is the of the line and (x_1,y_1) is a known point on the line. The first thing to do is to identify a point. Then, we can move from it while counting the rise and the run to find the slope.
In our example, we identify the point (0,1). We can see that when the run is 2 we have a rise of 3 units. Let's calculate the slope.
m = rise/run
m = 3/2
m = 1.5
Now we substitute the found values into the point-slope form to get our line equation.
y-y_1 = m (x-x_1)
y-1 = 1.5 (x-0)
y-1 = 1.5x
y= 1.5 x +1
The corresponding line equation for the example graph is y= 1.5 x +1.
Finding the Equation Using the Slope-Intercept Formula
We can also find the line equation using the .
y = mx + b
Here m is the slope of the line and b is the . Once again, let's start by identifying these features in the graph.
We now proceed to calculate the slope, just as we did above. We will not show that again, and we will just use its value — m=1.5. We can see from the graph that in this case, b=1. If we substitute these values into the slope-intercept form, we will find our line equation.
y = 1.5x + 1
