Answer:
The point slope form of the line is [tex]y-8=-\frac{2}{3}(x+3)[/tex].
Step-by-step explanation:
The slope intercept form of a line is
[tex]y=mx+b[/tex] .... (1)
where, m is slope and b is y-intercept.
The given equation is
[tex]y=-\frac{2}{3}x+6[/tex] .... (2)
From (1) and (2) it is clear that
[tex]m=-\frac{2}{3},b=6[/tex]
The slope of the line is [tex]-\frac{2}{3}[/tex].
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is slope.
The slope of the line is [tex]-\frac{2}{3}[/tex] and it passes through the point (-3,8).
[tex]y-8=-\frac{2}{3}(x-(-3))[/tex]
[tex]y-8=-\frac{2}{3}(x+3)[/tex]
Therefore the point slope form of the line is [tex]y-8=-\frac{2}{3}(x+3)[/tex].
