The slope-point form of line:
[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-9, 7) and (6, 2). Substitute:
[tex]m=\dfrac{2-7}{6-(-9)}=\dfrac{-5}{6+9}=-\dfrac{5}{15}=-\dfrac{1}{3}\\\\y-7=-\dfrac{1}{3}(x-(-9))\\\\\boxed{y-7=-\dfrac{1}{3}(x+9)}[/tex]
The slope-intercept form of line:
[tex]y=mx+b[/tex].
We have the slope m:
[tex]y=-\dfrac{1}{3}x+b[/tex]
Pu the coordinates of the point (6, 2) to the equation:
[tex]2=-\dfrac{1}{3}(6)+b[/tex]
[tex]2=-2+b[/tex] add 2 to both sides
[tex]4=b\to b=4[/tex]
[tex]\boxed{y=-\dfrac{1}{3}x+4}[/tex]
