The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-3, 7) and (9, -1). Substitute:
[tex]m=\dfrac{-1-7}{9-(-3)}=\dfrac{-8}{12}=-\dfrac{2}{3}[/tex]
Therefore we have
[tex]y=-\dfrac{2}{3}x+b[/tex]
Put the coordinates of the point (-3, 7) to the equation of a line:
[tex]7=-\dfrac{2}{3}(-3)+b[/tex]
[tex]7=2+b[/tex] subtract 2 from both sides
[tex]5=b[/tex]
Answer: [tex]\boxed{y=-\dfrac{2}{3}x+5}[/tex]
