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Question 1151534: what is the equation of a line that goes through (3,2) and (12,1)?
Found 3 solutions by Theo, josgarithmetic, Alan3354:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! first you want to find the slope.
slope = (y2-y1)/x2-x1)
let(x1,y1) = (3,2)
let(x2,y2) = (12,1)
this makes:
y2 = 1 and y1 = 2
x2 = 12 and x1 = 3
formula becomes (y2-y1)/(x2-x1) = (1-2)/(12-3) = -1/9
the slope intercept form of the equation for a straight line is y = mx + b
m is the slope and b is the y-intercept.
since the slope is -1/9, the formula becomes y = -1/9 * x + b
replace x and y with either one of the points on the line to find the value of b.
i used the point (3,2) to get 2 = -1/9 * 3 + b
simplify to get 2 = -3/9 + b
solve for b to get b = 2 + 3/9 = 18/9 + 3/9 = 21/9.
the equation of y = mx + b becomes y = -1/9 * x + 21/9
when x = 3, this equation becomes y = -1/9 * 3 + 21/9 which becomes y = -3/9 + 21/9 which becomes y = 18/9 which becomes y = 2 which is true.
when x = 12, this becomes y = -1/9 * 12 + 21/9 which becomes y = -12/9 + 21/9 which becomes y = 9/9 which becomes y = 1, which is true.
the equation is y = -1/9 * x + 21/9
that's your solution.
Answer by josgarithmetic(39616)  (Show Source):
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! what is the equation of a line that goes through (3,2) and (12,1)?
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| x y 1|
| 3 2 1| = 0
|12 1 1|
x*(2*1 - 1*1) - y*(3*1 - 12*1) + 1*(3*1 - 12*2) = 0
x + 9y - 21 = 0 is AN equation, not "the" equation.
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