Question 1053471
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It is ALWAYS possible to find a linear equation that passes through any two given points....<br>
The other tutor uses a seldom-used formula go get an equation in standard form, which is fine.<br>
I would use a different method, ending with an equation in slope-intercept form.<br>
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.<br>
(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.)<br>
To find the intercept we can use that slope and either of the given points.  Choosing (5,5)...<br>
y = mx+b
5 = (-2/3)(5)+b
5 = -10/3+b
b = 5+10/3 = (15+10)/3 = 25/3<br>
The slope-intercept form of the equation is<br>
y = (-2/3)x+25/3<br>