SOLUTION: Last question for now please and thank you. Given two points (-1,-5) and (-5,-4) how would I write the standard form of that first using point slope form? Thanks!

Question 134701: Last question for now please and thank you. Given two points (-1,-5) and (-5,-4) how would I write the standard form of that first using point slope form?
Thanks!
Answer by algebrapro18(249) (Show Source): You can put this solution on YOUR website!
Okay first you want to find the slope between those two points. The formula for slope is:

m = (y2-y1)/(x2-x1)

now from the ordered pair you get:

x1 = -1
x2 = -5
y1 = -5
y2 = -4

so now calculate m:

m = (-4-(-5))/(-5-(-1))
m = (-4+5)/(-5+1)
m = 1 / -4
m = -1/4

Now that we have our slope and a point(which point you choose doesn't matter you will get the same answer either way) we can plug into the point slope formula, which is:

y-y1=m(x-x1)

Using the values from before we get:

y-(-5) = -1/4(x-(-1))
y+5 = -1/4(x+1)

Now we need to solve for y here to get it into y=mx+b form and then from there we can get it into standard form.

y+5 = -1/4(x+1) --> Subtract 5 from both sides to isolate(solve) for y
y = -1/4(x+1)-5 --> Distribute the -1/4 into the (x+1)
y = -1/4x-1/4-5 --> Combine like terms
y = -1/4x-21/4

Now we need to get it into standard form so we need to do a few steps. But first just a reminder, standard form is ax+by = c where a,b,and c are integers(constants).

y = -1/4x-21/4 --> Multiply both sides by 4 to clear the fractions
4y = -x-21 --> Add x to both sides
x+4y = -21

Now we are done the standard form of that line is x+4y=-21. If you don't believe me we can check the work:

x1 = -1
y1 = -5

x+4y = -21
-1+4(-5) = -21
-1 + -20 = -21
-21 = -21

this one checks out, now lets try the other set

x2 = -5
y2 = -4

x+4y = -21
-5+4(-4) = -21
-5 + -16 = -21
-21 = -21

yes both these points checked out so we know we have the right answer.
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