How to derive the unique linear equation for any two coordinates
In short: Mastering coordinate geometry starts with understanding how to define a line. This video breaks down the step-by-step process of converting two simple points into a functional algebraic equation.
The video explains how to determine the equation of a straight line using the standard y=mx+c format. To do this, viewers first calculate the gradient (m) by dividing the 'rise' by the 'run', or more formally, by subtracting the y-coordinates and dividing by the difference in x-coordinates: (y2 - y1) / (x2 - x1).
Once the gradient is identified, it is substituted into the linear equation. By plugging in either of the original sets of coordinates for x and y, you can solve for 'c', the y-intercept. This systematic approach allows for the construction of a precise mathematical rule that describes any straight line passing through two specific points.
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Sources
- Summary by Intellect · source: Finding The Equation Of A Line Through 2 Points PART 1 | Graphs | Maths | FuseSchool
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