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| Equation of a Line |
Equation of a Line
For a Given Slope and y-intercept (Standard Form):
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:
y = mx+b
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.
For a Given Slope and One Point through which the Line Passes (Point-Slope Form):
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:
(y - y1) = m(x - x1)
To break this down a bit, substitute your slope value (ex. 2) in for m:
y=(2)x+b
Next, substitute your point (ex. (3,2)) in for x and y. Remember that the points are (x,y) in that order. Always.
(2)=2(3)+b
Solve for b. Then put the equation back into y=mx+b.
-4 = b
Therefor your final answer is: y=2x-4
For Two Points through which the Line Passes:
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:
(y - y1)(x2 - x1) = (y2 - y1)(x - x1)