The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
The slope-intercept form:
[tex]y=mx+b[/tex]
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (1, -5) and (-3, -7). Substitute:
[tex]m=\dfrac{7-(-5)}{-3-1}=\dfrac{12}{-4}=-3\\\\y-(-7)=-3(x-(-3))\\\\\boxed{y+7=-3(x+3)}[/tex]
Rewrite to the slope-intercept form:
[tex]y+7=-3(x+3)[/tex] use distributive property
[tex]y+7=-3x-9[/tex] subtract 7 from both sides
[tex]\boxed{y=-3x-16}[/tex]
