Question

The point-slope form of the equation of the line that passes through (-5, -1) and (10,-7) is

Answer 1

Answer:

2x + 5y = -15

Step-by-step explanation:

First, find the Rate of change [Slope]:

-y₁ + y₂\-x₁ + x₂ = m

1 - 7\5 + 10 = -⅖

Apply the Point-Slope Formula, y - y₁ = m(x - x₁), since we are given points. It does not matter which one you choose. NOTE: 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:

y + 7 = -⅖(x - 10)

y + 7 = -⅖x + 4

- 7 - 7

_________________

y = -⅖x - 3 >> Line in Slope-Intercept Form

Here it is in Standard Form:

y = -⅖x - 3

+⅖x +⅖x

____________

⅖x + y = -3 [We do not want fractions in our Standard Equations, so multiply by the denominator to get rid of it.]

5[⅖x + y = -3]

2x + 5y = -15 >> Line in Standard Form

__________________________________________________________

y + 1 = -⅖(x + 5)

y + 1 = -⅖x - 2

- 1 - 1

________________

y = -⅖x - 3 Line in Slope-Intercept Form

y = -⅖x - 3

+⅖x +⅖x

___________

⅖x + y = -3 [We do not want fractions in our Standard Equations, so multiply by the denominator to get rid of it.]

5[⅖x + y = -3]

2x + 5y = -15 >> Line in Standard Form

** You see? I told you it did not matter which ordered pair you choose because you will always get the EXACT SAME RESULT.

I am joyous to assist you anytime.