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