SOLUTION: Find an equation in slope-intercept form passing through the points (2,5) and (7,-3).

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Question 46532: Find an equation in slope-intercept form passing through the points (2,5) and (7,-3).
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The 2 points alone will give you the slope.
m+=+%28y%282%29+-+y%281%29%29+%2F+%28x%282%29+-+x%281%29%29 where m is the slope.
The points given are in the form
(2,5) = x(2), y(2) and
(7, -3) = x(1), y(1))
so
m+=+%285+-+%28-3%29%29+%2F+%282+-+7%29
m+=+8+%2F+-5
m+=+-%288%2F5%29
Now you need something that equals the slope, but is
general in form and applies to any x or y.
m+=+%28y+-+y%281%29%29+%2F+%28x+-+x%281%29%29
This is perfectly true as long as x and y are on the line passing
through (2,5) and (7,-3). To make that so, set it equal to the
value of m you got from m+=+%28y%282%29+-+y%281%29%29+%2F+%28x%282%29+-+x%281%29%29
-%288%2F5%29+=+%28y+-+y%281%29%29+%2F+%28x+-+x%281%29%29
-%288%2F5%29+=+%28y+-+%28-3%29%29+%2F+%28x+-+7%29
Now you can put it in the form y = mx + b
multiply both sides by (x - 7)
-%288%2F5%29%2Ax+%2B+%2856%2F5%29+=+y+%2B+3
-8x+%2B+56+=+5y+%2B+15
5y+=+-8x+%2B+41
y+=+-%288%2F5%29x+%2B+41%2F5 this is the answer
The slope m is correct. Check to see if b = 41/5 is correct by setting
x = 0 in the slope formula
-%288%2F5%29+=+%28y+-+%28-3%29%29+%2F+%280+-+7%29
56%2F5+=+y+%2B+3
y+=+56%2F5+-+3
y+=+56%2F5+-+15%2F5
y+=+41%2F5
checks OK