Question

What is the equation for the line that passes through the points (-5, 2) and (5,-6)?​

Answer 1

4x + 5y = -10 or y = -⅘x - 2

Explanation:

First, find the rate of change [slope]:

-y₁ + y₂\-x₁ + x₂ = m

`( -2 - 6)/(5 + 5) = - (8)/(10) = - (4)/(5)`

Then use the Point-Slope Formula since we are given points. Now, according to this formula, all negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY careful inserting the coordinates into the formula with their CORRECT signs. It does not matter which one you choose:

y - y₁ = m(x - x₁)

y + 6 = -⅘(x - 5)

y + 6 = -⅘x + 4

- 6 - 6

_______________

y = -⅘x - 2

If you want it in Standard Form:

y = -⅘x - 2

+⅘x +⅘x

___________

⅘x + y = -2 [We do not want fractions in our Standard Equations, so multiply by the denominator to get rid of it.]

5[⅘x + y = -2]

4x + 5y = -10 >> Line in Standard Form

__________________________________________________________

y - 2 = -⅘(x + 5)

y - 2 = -⅘x - 4

+ 2 + 2

______________

y = -⅘x - 2

y = -⅘x - 2

+⅘x +⅘x

___________

⅘x + y = -2 [We do not want fractions in our Standard Equations, so multiply by the denominator to get rid of it.]

5[⅘x + y = -2]

4x + 5y = -10 >> Line in Standard Form

** You see? I told you that it would not matter which ordered pair you choose because you will always get the exact same result!!!

I am joyous to assist you anytime.