What is the equation of the line passing through the points (–2, 2) and (3, –1)

3x + 5y = 4 or y = -⅗x + ⅘

Step-by-step explanation:

First, find the Rate of change [Slope]:

-y₁ + y₂\-x₁ + x₂ = m

-2 - 1\2 + 3 = -⅗

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 + 1 = -⅗(x - 3)

y + 1 = -⅗x + 1⅘

- 1 - 1

y = -⅗x + ⅘ >> Line in Slope-Intercept Form

If you want it in Standard Form:

y = -⅗x + ⅘

+⅗x +⅗x

⅗x + y = ⅘ [We do not want fractions in our Standard Equations, so multiply by the denominator to get rid of it.]

5[⅗x + y = ⅘]

3x + 5y = 4 >> Line in Standard Form

y - 2 = -⅗(x + 2)

y - 2 = -⅗x - 1⅕

+ 2+ 2

y = -⅗x + ⅘ [We do not want fractions in our Standard Equations, so multiply by the denominator to get rid of it.]

5[⅗x + y = ⅘]

3x + 5y = 4 >> Line in Standard Form

I am joyous to assist you anytime.

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

2nd one in the first row is correct