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Question 158780: How do i find the equation of a line, for example a line through points (1,-6) and (4,3). I have no idea how to find the equation, thanx to a few absences.
Thank you,
John
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! if the line goes through (1,-6) and (4,3), then the x coordinates are 1 and 4, and the y coordinates are -6 and 3.
let x1 = 1,
let y1 = -6
let x2 = 4
let y2 = 3
slope-intercept form of the equation would be y = m*x + b where m is the slope and b is the y-intercept when x = 0.
formula for slope is (y2-y1)/(x2-x1)
this equals (3-(-6))/(4-1) which equals 9/3 which equals 3.
the slope of the equation = 3 = m
so the slope-intercept form of the equation is y = 3*x + b
to find b, you need to solve the equation for one of the points given.
take (1,-6)
this makes y = 3*x + b equal to -6 = 3*1 + b
this makes b = -9.
y-intercept form of the equation is therefore y = 3*x-9
substituting in the other set of points of the line, we get
3 = 3*4-9 = 12-9 = 3 which means the equation is good because we have an identity.
so you have the y-intercept form of the equation is y = 3*x-9.
to transform this to the standard form of the equation, we need to make it look like a*x + b*y = c where a,b,c are constants.
subtracting 3*x from both sides of the equation gets
-3*x + y = -9
since this satisfies the form of the standard equation we can stop here.
solving for one of the points, we use (1,-6) and we get
-3*1 + (-6) = -9 which becomes
-3-6=-9
which becomes
-9=-9 proving the standard form of the equation is accurate.
you have 2 forms of the same equation
y = 3*x-9 is the slope-intercept form.
-3*x+y=-9 is the standard form.
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