Straight Line Between Two Points.xls
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Description
Purpose of calculation:
Find equation of a line given 2 coordinates
Calculation Reference
First principles
Calculation Validation
Independently checked.
Calculation Reference
Coordinate Geometry
Geometry of 2 Dimensions
To find the equation of a line given two coordinates, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is one of the given coordinates, and m is the slope of the line.
To find the slope of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x2, y2) is the other given coordinate.
Once we have the slope, we can substitute it and one of the given coordinates into the point-slope form to get the equation of the line:
y - y1 = m(x - x1)
or we can rearrange it into the slope-intercept form:
y = mx + b
where b = y1 - mx1 is the y-intercept.
So, given two coordinates (x1, y1) and (x2, y2), the equation of the line passing through them is:
y - y1 = (y2 - y1) / (x2 - x1) * (x - x1)
or
y = (y2 - y1) / (x2 - x1) * (x - x1) + y1
or
y = mx + b
where m = (y2 - y1) / (x2 - x1) and b = y1 - m * x1.
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