The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have (-6, -8), (12, 7).
Substitute:
[tex]m=\dfrac{7-(-8)}{12-(-6)}=\dfrac{7+8}{12+6}=\dfrac{15}{18}=\dfrac{5}{6}[/tex]
The slope-point form:
[tex]y-y_1=m(x-x_1)[/tex]
We have m = 5/6 and (12, 7).
Substitute:
[tex]y-7=\dfrac{5}{6}(x-12)[/tex]
The slope-intercept form:
[tex]y=mx+b[/tex]
[tex]y-7=\dfrac{5}{6}(x-12)\\\\y-7=\dfrac{5}{6}x-\dfrac{5}{6}\cdot12}\\\\y-7=\dfrac{5}{6}x-\dfrac{5}{1}\cdot2\\\\y-7=\dfrac{5}{6}x-10\qquad|+7\\\\y=\dfrac{5}{6}x-3[/tex]
