GIven:
The given points are (6,-6) and (8,-3).
The objective is to find the equation of the line in slope intercept form.
Consider the given points are,
[tex]\begin{gathered} (x_1,y_1)=(6,-6) \\ (x_2,y_2)=(8,-3) \end{gathered}[/tex]The general equation for straight line through two points is,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \end{gathered}[/tex]Here, m represents the slope of the equation.
On plugging the values in the above equation,
[tex]\begin{gathered} y-(-6)=\frac{-3-(-6)}{8-6}(x-6) \\ y+6=\frac{-3+6}{2}(x-6) \\ y=\frac{3}{2}(x-6)-6 \\ y=\frac{3x}{2}-\frac{3\times6}{2}-6 \\ y=\frac{3x}{2}-9-6 \\ y=\frac{3x}{2}-15 \end{gathered}[/tex]Hence, the equation of line in slope intercept form is y = (3/2)x-15.
