SOLUTION: Find the standard form of the equation of the line that passes through the points (0, -1) and (8, 8).

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Question 173087: Find the standard form of the equation of the line that passes through the points (0, -1) and (8, 8).
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%288--1%29%2F%288-0%29 Plug in y%5B2%5D=8, y%5B1%5D=-1, x%5B2%5D=8, and x%5B1%5D=0


m=%289%29%2F%288-0%29 Subtract -1 from 8 to get 9


m=%289%29%2F%288%29 Subtract 0 from 8 to get 8


So the slope of the line that goes through the points and is m=9%2F8


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--1=%289%2F8%29%28x-0%29 Plug in m=9%2F8, x%5B1%5D=0, and y%5B1%5D=-1


y%2B1=%289%2F8%29%28x-0%29 Rewrite y--1 as y%2B1


y%2B1=%289%2F8%29x-%289%2F8%29%280%29 Distribute


y%2B1=%289%2F8%29x-0 Multiply


y%2B1=%289%2F8%29x Simplify


y-%289%2F8%29x=-1 Subtract %289%2F8%29x from both sides. Subtract 1 from both sides.


-%289%2F8%29x%2By=-1 Rearrange the terms.


-9x%2B8y=-8 Multiply EVERY term by the LCD 8 to clear the fraction.


9x-8y=8 Multiply EVERY term by -1 to make the "x" coefficient positive.


So now the equation is in standard form Ax%2BBy=C where A=9, B=-8, and C=8

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the standard form of the equation of the line that passes through the points (0, -1) and (8, 8).
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I know 2 ways to do this.
One:
Find the slope, m
m = (diff in y)/(diff in x)
m = (8-(-1))/8
m = 9/8
Use either point
y-y1 = m*(x-x1)
y-8 = (9/8)*(x-8
y-8 = 9x/8 - 9
8y - 64 = 9x - 72
9x - 8y = 8
Two:
Use determinants
|x y +1|
|0 -1 1| = 0
|8 +8 1|
x(-1-8) - y(0-8) +(8) = 0
-9x +8y = -8
9x - 8y = 8