Answer :
Answer:
The equation of the line in slope-intercept form is;
[tex]y=-\frac{2}{3}x+6[/tex]Explanation:
We want to find the equation of the line with the slope and a point given.
[tex]\begin{gathered} \text{slope m=}\frac{-2}{3} \\ \text{ point (-3,8)} \end{gathered}[/tex]Recall that the point-slope equation of a straight line is of the form;
[tex]y-y_1=m(x-x_1)[/tex]substituting the given slope and point into the equation and simplifying;
[tex]\begin{gathered} y-8=-\frac{2}{3}(x-(-3)) \\ y-8=-\frac{2}{3}(x+3) \\ y=-\frac{2}{3}x-\frac{2}{3}(3)+8 \\ y=-\frac{2}{3}x-2+8 \\ y=-\frac{2}{3}x+6 \end{gathered}[/tex]Therefore, the equation of the line in slope-intercept form is;
[tex]y=-\frac{2}{3}x+6[/tex]