Answer:
![y = \dfrac{-1}{4}x + \dfrac{-27}{4}](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac%7B-1%7D%7B4%7Dx%20%2B%20%5Cdfrac%7B-27%7D%7B4%7D)
Step-by-step explanation:
The equation of a line is:
y = mx + b
Where:
m = slope
b = y-intercept
First thing we need to do is solve for the slope. The slope formula is:
![m = \dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Where:
x₁ = x-coordinate of the first point
x₂ = x-coordinate of the second point
y₁ = y-coordinate of the first point
y₂ = y-coordinate of the second point
We are given the following points:
Point 1: (-3, -6)
Point 2: (5, -8)
So let's plug in our coordinates into the slope formula:
![m = \dfrac{y_2-y_1}{x_2-x_1}\\\\ =\dfrac{(-8)-(-6)}{5-(-3)}\\\\ =\dfrac{-2}{8}\\\\ =\dfrac{-1}{4}](https://tex.z-dn.net/?f=m%20%3D%20%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%5C%5C%20%20%20%20%3D%5Cdfrac%7B%28-8%29-%28-6%29%7D%7B5-%28-3%29%7D%5C%5C%5C%5C%20%20%20%20%3D%5Cdfrac%7B-2%7D%7B8%7D%5C%5C%5C%5C%20%3D%5Cdfrac%7B-1%7D%7B4%7D)
So we have our new equation of this line:
![y = \dfrac{-1}{4}x + b](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac%7B-1%7D%7B4%7Dx%20%2B%20b)
What do we do then about the y-intercept?
Our points will help us out by plugging them in our equation, so we can solve for our y-intercept (b).
Let's do both to show that it would be the same:
Point 1 (-3, -6)
![y = \dfrac{-1}{4}x + b\\\\-6 = \dfrac{-1}{4}(-3) + b\\\\-6 = \dfrac{3}{4} + b\\\\-6 = \dfrac{3}{4} + b\\\\subtract \dfrac{3}{4}\;from\;both\;sides\;of\;the\;equation\\\\-6- \dfrac{3}{4}= \dfrac{3}{4}- \dfrac{3}{4}+b\\\\\\\dfrac{-24-3}{4}=0+b\\\\\\-\dfrac{27}{4} = b](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac%7B-1%7D%7B4%7Dx%20%2B%20b%5C%5C%5C%5C-6%20%3D%20%5Cdfrac%7B-1%7D%7B4%7D%28-3%29%20%2B%20b%5C%5C%5C%5C-6%20%3D%20%5Cdfrac%7B3%7D%7B4%7D%20%2B%20b%5C%5C%5C%5C-6%20%3D%20%5Cdfrac%7B3%7D%7B4%7D%20%2B%20b%5C%5C%5C%5Csubtract%20%5Cdfrac%7B3%7D%7B4%7D%5C%3Bfrom%5C%3Bboth%5C%3Bsides%5C%3Bof%5C%3Bthe%5C%3Bequation%5C%5C%5C%5C-6-%20%5Cdfrac%7B3%7D%7B4%7D%3D%20%5Cdfrac%7B3%7D%7B4%7D-%20%5Cdfrac%7B3%7D%7B4%7D%2Bb%5C%5C%5C%5C%5C%5C%5Cdfrac%7B-24-3%7D%7B4%7D%3D0%2Bb%5C%5C%5C%5C%5C%5C-%5Cdfrac%7B27%7D%7B4%7D%20%3D%20b)
Point 2: (5, -8)
![y = \dfrac{-1}{4}x + b\\\\-8 = \dfrac{-1}{4}(5) + b\\\\-8 = \dfrac{-5}{4} + b\\\\-8 = \dfrac{-5}{4} + b\\\\subtract \dfrac{-5}{4}\;from\;both\;sides\;of\;the\;equation\\\\-8- \dfrac{-5}{4}= \dfrac{-5}{4}- \dfrac{-5}{4}+b\\\\\\\dfrac{-32-(-5)}{4}=0+b\\\\\\\dfrac{-27}{4} = b](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac%7B-1%7D%7B4%7Dx%20%2B%20b%5C%5C%5C%5C-8%20%3D%20%5Cdfrac%7B-1%7D%7B4%7D%285%29%20%2B%20b%5C%5C%5C%5C-8%20%3D%20%5Cdfrac%7B-5%7D%7B4%7D%20%2B%20b%5C%5C%5C%5C-8%20%3D%20%5Cdfrac%7B-5%7D%7B4%7D%20%2B%20b%5C%5C%5C%5Csubtract%20%5Cdfrac%7B-5%7D%7B4%7D%5C%3Bfrom%5C%3Bboth%5C%3Bsides%5C%3Bof%5C%3Bthe%5C%3Bequation%5C%5C%5C%5C-8-%20%5Cdfrac%7B-5%7D%7B4%7D%3D%20%5Cdfrac%7B-5%7D%7B4%7D-%20%5Cdfrac%7B-5%7D%7B4%7D%2Bb%5C%5C%5C%5C%5C%5C%5Cdfrac%7B-32-%28-5%29%7D%7B4%7D%3D0%2Bb%5C%5C%5C%5C%5C%5C%5Cdfrac%7B-27%7D%7B4%7D%20%3D%20b)
Now that we have b, we can insert that into the equation of the line:
![y = \dfrac{-1}{4}x + b\\\\y = \dfrac{-1}{4}x + \dfrac{-27}{4}](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac%7B-1%7D%7B4%7Dx%20%2B%20b%5C%5C%5C%5Cy%20%3D%20%5Cdfrac%7B-1%7D%7B4%7Dx%20%2B%20%5Cdfrac%7B-27%7D%7B4%7D)