Answer:
[tex]y=\frac{1}{3}x-8[/tex]
Step-by-step explanation:
Slope-intercept form of an equation is written as [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
The slope of a line that passes through the points [tex](x_1,\: y_1)[/tex] and [tex](x_2, \: y_2)[/tex] is [tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]. Using the coordinates [tex](6,-6)[/tex] and [tex](9,-5)[/tex] as given in the problem, we have slope of this line to be:
[tex]m=\frac{-5-(-6)}{9-6}=\frac{1}{3}[/tex].
Now using this slope we've found and any point the line passes through, we can find the y-intercept of this equation:
[tex]-6=\frac{1}{3}(6)+b, \\ b=-8[/tex]
Therefore, the equation of this line in slope-intercept form is [tex]\fbox{$y=\frac{1}{3}x-8$}[/tex].
