How to calculate the Slope Intercept equation from two points
A common problem in linear equations is of how to determine the equation of a line, when given any two points on that line.
Here's a simple step by step guide on how to work out the equation in Slope Intercept Form (y = mx + b)
For example, given the two points (1,5) and (3,1), let's work out the solution. Lets call the (1,5) "Point 1" and (3,1) "Point 2" for reference.
Step 1: Determine the Slope (m)
The Slope of a line is determined by the change in the value of y which corresponds to a given change in the value of x. We can use the two points we have been given to determine the slope:
|Point2.y - Point1.y|
|Point2.x - Point1.x|
Substituting our values for the Point:
|1 - 5|
|3 - 1|
Step 2: Determining the Y-Intercept (b)
The Y intercept is the point where the line intercepts the Y Axis (which is where x = 0). So by using this definition, and EITHER of the two points, we can work back from the point
Our slope, m, is -2. This means for every 1 unit of x we increase, y will decrease by 2 y-units (since m is -2), and conversely, for every x-unit we decrease, y will increase by 2 y-units (since -1 x -2 = 2)!
Taking the first point (1,5), x is 1. To get to the Y axis, we need to subtract 1 x-unit, so a decrease of 1 x-unit will require an increase of 2 y-units.
So the Y Intercept is 5 + 2 = 7
In mathematical terms, the general form of working a point back to the Y Axis using the slope of the line is:
Taking Point 1, (1,5)
Note that you could have ALSO used Point2, (3, 1):
So our final equation for the line through the points (1,5) and (3,1), in Slope-Intercept form, is
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