Write an equation in point-slope form and in slope-intercept form.

The point-slope form:
[tex]y-y_1=m(x-x_1)\\\\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-(-5)=-3(x-1)\\\\\boxed{y+5=-3(x-1)}[/tex]
The slope-intercept form:
[tex]y=mx+b[/tex]
[tex]y+5=-3(x-1)[/tex] use distributive property
[tex]y+5=-3x+3[/tex] subtract 5 from both sides
[tex]\boxed{y=-3x-2}[/tex]