Question 132579: find the equation of the line passing through the points
a. (1,3) et (3,6)
b. (-2, -5) et (4,2)
c. (2,6) et (4,2)
d. (0,0) et (4,6)
e. (-5,-1) et (7,-5)
f. (1,1) et (7,7)
g. (-2,0) et (3,6)
h. (3,-1) et (-2,1)
i. (-3,0) et (0,-3)
j. (4,4) et (-3,8)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Let's get one thing clear right off the bat. This site is NOT a homework machine put here so that you don't have to think or do any work. I'll do one of these and you should be able to do the rest of them.
Given two points, you can substitute the coordinates of the points into the two-point form of the line to derive an equation of the line passing through the two points.
Two-point form: 
It doesn't matter which point you call number 1 and which you call number two as long as you are consistent.
Let's do item g. (-2,0) et (3,6). And let's say that (-2,0) is point number 1. That means that:
 ,
 ,
 , and
Now substitute:
Do the arithmetic:
Multiply by the denominator of the fraction:
Distribute the coefficient on the binomial:
Add the negative of the x term to both sides:
And that is your standard form equation for the line passing through (-2,0) and (3,6). You could also multiply by -1 to obtain  , if you like.
Do the others the same way. Just be careful with the signs when you substitute into the two-point form and when you do the required arithmetic.
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