38 lines
1.3 KiB
Markdown
38 lines
1.3 KiB
Markdown
---
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title: Equation of a Line
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---
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## Equation of a Line
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### For a Given Slope and y-intercept (Standard Form):
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Let `m` be the slope of the line, and `b` be the y-intercept. (Note that the y-intercept is the point at which the given line crosses the y-axis). Then the equation of a line is:
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`y = mx+b`
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Keep in mind that you still have `y` which is the Dependant Variable and `x` the Independant Variable meaning that `x` can be any value, whereas `y` will be a value based off of what `x` is.
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### For a Given Slope and One Point through which the Line Passes (Point-Slope Form):
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Let `m` be the slope of the line and `(x1, y1)` be the co-ordinate of the point through which the given line passes. Then the equation of a line is:
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`(y - y1) = m(x - x1)`
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To break this down a bit, substitute your slope value (ex. 2) in for m:
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`y=(2)x+b`
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Next, substitute your point (ex. (3,2)) in for `x` and `y`. Remember that the points are `(x,y)` in that order. Always.
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`(2)=2(3)+b`
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Solve for `b`. Then put the equation back into `y=mx+b`.
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`-4 = b`
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Therefor your final answer is: `y=2x-4`
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### For Two Points through which the Line Passes:
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Let `(x1, y1)` and `(x2, y2)` be the co-ordinates of two points through which the given line passes. Then the equation of a line is:
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`(y - y1)(x2 - x1) = (y2 - y1)(x - x1) `
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