Answer:
\(y+6=\frac{1}{3}(x+2)\)
Step-by-step explanation:
General equation of point slope form : \(y-y_1=m(x-x_1)\)
where m is the slope
Point = \((x_1,y_1)=(-2,-6)\)
Slope = \(m = \frac{1}{3}\)
Substitute the values in general form of point slope form .
\(y-y_1=m(x-x_1)\)
\(y-(-6)=\frac{1}{3}(x-(-2))\)
\(y+6=\frac{1}{3}(x+2)\)
This can be simplified further
\(y+6=\frac{1}{3}x+\frac{2}{3}\)
\(y=\frac{1}{3}x+\frac{2}{3}-6\)
\(y=\frac{1}{3}x-\frac{16}{3}\)
Hence the equation of a line, in point-slope form, that passes through (−2, −6) and has a slope of 1/3 is \(y+6=\frac{1}{3}(x+2)\)
