Question 1053471: Given the set of information, find a linear equation satisfying the conditions, if possible. (If not possible, enter IMPOSSIBLE.)
passes through (x, y) = (−1, 9) and (x, y) = (5, 5)
Y= _______
Found 2 solutions by mananth, greenestamps:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! passes through (x1, y1) = (−1, 9) and (x2, y2) = (5, 5)
Use the formula
(x+1)/-6 = (y-9)/4
4(x+1)=-6(y-9)
4x+4 =-6y+54
4x+6y=50
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
It is ALWAYS possible to find a linear equation that passes through any two given points....
The other tutor uses a seldom-used formula go get an equation in standard form, which is fine.
I would use a different method, ending with an equation in slope-intercept form.
From the first point to the second, the run (change in x) is 6 (from -1 to 5) and the rise (change in y) is -4 (from 9 to 5). So the slope (rise/run) is -4/6 or -2/3.
(Note that I prefer determining the slope using the definition ("rise over run"), as opposed to plugging numbers into the formula for calculating slope. If I use the formula on 1000 problems, I will get the wrong slope a few times out of carelessness or silly arithmetic errors; I will never get the wrong slope using the definition.)
To find the intercept we can use that slope and either of the given points. Choosing (5,5)...
y = mx+b
5 = (-2/3)(5)+b
5 = -10/3+b
b = 5+10/3 = (15+10)/3 = 25/3
The slope-intercept form of the equation is
y = (-2/3)x+25/3
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