Question 168213
write the slope-intercept form of a linear equation, passing through each pair of points
(5,1) and (1,9)
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There are 2 ways to do this.
The long way:
Find the slope (m) of the line thru the 2 points
m = (y2-y1)/(x2-x1)
m = (1-9)/(5-1)
m = -8/4 = -2
Then use either point and the slope:
y-y1 = m*(x-x1)
y - 1 = -2*(x-5)
y-1 = -2x + 10
y = -2x + 11  (slope-intercept form)
2x + y = 11 (standard form)
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The easier way, using determinants:
|x y 1|
|1 9 1| = 0
|5 1 1|
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x*(9-1) -y*(1-5) + 1*(1-45) = 0
8x + 4y -44 = 0
2x + y = 11 (standard form)