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

4x + 5y = -10 or y = -⅘x - 2

Step-by-step explanation:

First, find the rate of change [slope]:

-y₁ + y₂\-x₁ + x₂ = m

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.

i believe it is c.y = 9x

rise over run. 9 units up over 1 unit right or 9/1

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1