The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points
[tex](-3,\ -2);\ (5,\ 4)[/tex]
Substitute:
[tex]m=\dfrac{4-(-2)}{5-(-3)}=\dfrac{6}{8}=\dfrac{3}{4}[/tex]
The point slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute:
[tex]y-(-2)=\dfrac{3}{4}(x-(-3))\\\\y+2=\dfrac{3}{4}x+\dfrac{9}{4}\ \ \ \ |-2\\\\y=\dfrac{3}{4}x+\dfrac{9}{4}-\dfrac{8}{4}\\\\\boxed{y=\dfrac{3}{4}x+\dfrac{1}{4}}[/tex]
