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. :]

Hi there!

A line parallel to y = 8/3x has a slope of 8/3, therefore:

Plug the given slope into the slope-intercept formula, along with the given coordinates to solve for the formula:

2 = 8/3(1) + b

2 = 8/3 + b

6/3 = 8/3 + b

6/3 - 8/3 = b

b = -2/3

Therefore, the equation in slope formula is:

y = 8/3x - 2/3