The equation of the line passing through the given points in the point slope form is;
[tex]y-6\text{ = }\frac{14}{3}(x\text{ + 6)}[/tex]Here, we want to find the equation of the line that passes through the given points
Mathematically, we can write the equation of a line as follows in point slope form;
[tex]y-y_1=m(x-x_1)[/tex]m here represents the slope of the line
To calculate m which is the slope, we use the slope equation as follows;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ m\text{ = }\frac{6-(-8)}{-6-(-9)}\text{ = }\frac{6\text{ + 8}}{-6\text{ + 9}}\text{ = } \\ =\text{ }\frac{14}{3} \end{gathered}[/tex]To write the equation, we use any of the two given points.
Thus, we have;
[tex]\begin{gathered} y-6\text{ = }\frac{14}{3}(x-(-6)) \\ \\ y-6\text{ = }\frac{14}{3}(x\text{ + 6)} \end{gathered}[/tex]