SOLUTION: I am supposed to write an equation in standard form of the line passing through these points. (1,-1) and (5,6). PLEASE HELP!!!!!! The answer is -7x+4y=-11, but I don't know how to

Algebra ->  Graphs -> SOLUTION: I am supposed to write an equation in standard form of the line passing through these points. (1,-1) and (5,6). PLEASE HELP!!!!!! The answer is -7x+4y=-11, but I don't know how to       Log On


   

Question 128025This question is from textbook algebra: structure and method: book1
: I am supposed to write an equation in standard form of the line passing through these points. (1,-1) and (5,6). PLEASE HELP!!!!!! The answer is -7x+4y=-11, but I don't know how to get there. HELP MUCH APPRECIATED!!!! This question is from textbook algebra: structure and method: book1

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You are given P%5B1%5D(x%5B1%5D,y%5B1%5D) and P%5B2%5D(x%5B2%5D,y%5B2%5D). Which point you assign the designation P%5B1%5D and which you assign P%5B2%5D doesn't make any difference as long as you keep it consistent as you work the problem.

So lets say P%5B1%5D is (1,-1) and P%5B2%5D is (5,6).

That means:
x%5B1%5D=1
y%5B1%5D=-1
x%5B2%5D=5
y%5B2%5D=6

The equation for a line through two points is given by:

y-y%5B1%5D=%28%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29%29%28x-x%5B1%5D%29

Just substitute the numbers:
y-%28-1%29=%28%28%28-1%29-6%29%2F%281-5%29%29%28x-1%29

And do the arithmetic:
y%2B1=%28%28-7%29%2F%28-4%29%29%28x-1%29
y%2B1=%287%2F4%29%28x-1%29

Now we need to put the equation into standard form. Standard form is Ax%2BBy=c

y%2B1=%287%2F4%29%28x-1%29

Multiply both sides by 4:
4%28y%2B1%29=7%28x-1%29

Distribute and remove parentheses:
4y%2B4=7x-7

Add -7x to both sides:
-7x%2B4y%2B4=-7

Add -4 to both sides:
-7x%2B4y=-11

Actually that is good enough, but I would multiply both sides by -1, just because it is neater.
7x-4y=11

Ah yes, Monk would approve.

Check the answer:
If the line represented by the derived equation actually passes through the two given points, each of the sets of given x- and y-coordinates will make the equation a true statement when substituted.

So. 7%281%29-4%28-1%29=7%2B4=11, so the first point makes the equation true. And 7%285%29-4%286%29=35-24=11, so the second point makes the equation true. Answer checks.