Find the equation of the line: through (5,-1) and(2,2)

Answer 1

Or...First find slope:

m = (y₂ - y₁)/(x₂ - x₁)

So,

m = (2 - (-1)) / ( 2 - 5) = 3/(-3) = -1

Now, use y - y₁ = m(x - x₁) where (x₁, y₁) is either of the two points you have, I'll use (2,2)

y - 2 = (-1)(x - 2) <----Now simplify.

y - 2 = -x + 2

x + y - 2 = 2

x + y = 4 <----same answer as above without any of the hassle.

Hope this helps

Mr. K

Answer 2

(y+1)/(x-5) = (y-2)/(x-2) these are two expressions for the slope using each point on either side

cross multiply

xy + x -2y -2 = xy -2x -5y +10

simplify and cancel the xy terms

3x +3y =12 divide by 3

x + y = 4

check the answer. Plug in each point and see if it fits that equation (5,-1) and (2,2)

5-1=4 and 2+2=4. It works