SOLUTION: find the equation of the line passing through (2,1) and (-3,5). find the x and y intercepts. thankyouuu

Algebra ->  Equations -> SOLUTION: find the equation of the line passing through (2,1) and (-3,5). find the x and y intercepts. thankyouuu      Log On


   

Question 610080: find the equation of the line passing through (2,1) and (-3,5). find the x and y intercepts. thankyouuu
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First, choose the form of the equation.
+y+=+m%2Ax+%2B+b+ is the slope-intercept form
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The line goes through (2,1), so I can say
(1) +1+=+m%2A2+%2B+b+
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The line goes through (-3,5), so I can say
(2) +5+=+m%2A%28-3%29+%2B+b+
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(1) +2m+%2B+b+=+1+
(2) +-3m+%2B+b+=+5+
Subtract (2) from (1)
(1) +2m+%2B+b+=+1+
(2) +3m+-+b+=+-5+
+5m+=+-4+
+m+=+-4%2F5+
So far I have
+y+=+%28-4%2F5%29%2Ax+%2B+b+
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Now plug (x,y) in from either of the 2 points
(2,1)
+1+=+%28-4%2F5%29%2A2+%2B+b+
+1+=+-8%2F5+%2B+b+
+b+=+5%2F5+%2B+8%2F5+
+b+=+13%2F5+
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The equation of the line is:
+y+=+%28-4%2F5%29%2Ax+%2B+13%2F5+
---------------------
check:
(2,1)
+1+=+%28-4%2F5%29%2A2+%2B+13%2F5+
+1+=+-8%2F5+%2B+13%2F5+
+1+=+5%2F5+
+1=1+
--------
(-3,5)
+5+=+%28-4%2F5%29%2A%28-3%29+%2B+13%2F5+
+5+=+12%2F5+%2B+13%2F5+
+25+=+12+%2B+13+
+25+=+25+
OK