<u>Answer:</u>
The equation of a line, in point slope form that passes through (-2, -6) and has a slope of 1/3 is ![y+6=\frac{1}{3}(x+2)](https://tex.z-dn.net/?f=y%2B6%3D%5Cfrac%7B1%7D%7B3%7D%28x%2B2%29)
<u>Solution:</u>
Given that line passes through (-2, -6) and has slope of 1/3
We have to find the equation of the line
The point slope form is given as
![y-b=m(x-a)](https://tex.z-dn.net/?f=y-b%3Dm%28x-a%29)
where m is the slope of the line and a, b are the x, y coordinates of the given point through which the line passes.
Here in this question, m = 1/3 and a = -2 and b = -6
By substituting in point slope form we get,
![y - (-6) = \frac{1}{3}(x - (-2))\\\\y + 6 = \frac{1}{3}(x + 2)](https://tex.z-dn.net/?f=y%20-%20%28-6%29%20%3D%20%5Cfrac%7B1%7D%7B3%7D%28x%20-%20%28-2%29%29%5C%5C%5C%5Cy%20%2B%206%20%3D%20%5Cfrac%7B1%7D%7B3%7D%28x%20%2B%202%29)
Hence the equation of a line, in point slope form that passes through (-2, -6) and has a slope of 1/3 is ![y+6=\frac{1}{3}(x+2)](https://tex.z-dn.net/?f=y%2B6%3D%5Cfrac%7B1%7D%7B3%7D%28x%2B2%29)