Question 22434
<pre>Write an equation for the line containing
1.(3,17) and (-5,-23)
2.(3,-10)(7,-22)
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For these you need 
1. the slope formula:

     y<sub>2</sub> - y<sub>1</sub>
m = —————————
     x<sub>2</sub> - x<sub>1</sub>

2.  The point-slope form of the equation of a line:

y - y<sub>1</sub> = m(x - x<sub>1</sub>)

1.(3,17) and (-5,-23)

Here

 (x<sub>1</sub>,y<sub>1</sub>) = (3,17) so x<sub>1</sub> = 3 and y<sub>1</sub> = 17
 (x<sub>2</sub>,y<sub>2</sub>) = (-5,-23) so x<sub>2</sub> = -5 and y<sub>2</sub> = -23

     y<sub>2</sub> - y<sub>1</sub>
m = —————————
     x<sub>2</sub> - x<sub>1</sub>

     (-23) - (17)
m = ——————————————
      (-5) - (3)

     -40
m = ————— = 5
     -8

Now use

y - y<sub>1</sub> = m(x - x<sub>1</sub>)

Substitute only for x<sub>1</sub>, y<sub>1</sub> and m.  Do not substitute anything
for x or y.

y - (17) = 5(x - 3)

  y - 17 = 5x - 15

       y = 5x + 2
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2.(3,-10)(7,-22)
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This is exactly like the first one.

The answer is 

       y = -3x - 1

Edwin
AnlytcPhil@aol.com</pre>