Answer:
[tex]\large\boxed{y-3=-(x+4)}\\or\\\boxed{y+4=-(x-3)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (-4, 3) and (3, -4).
Substitute:
[tex]m=\dfrac{-4-3}{3-(-4)}=\dfrac{-7}{7}=-1[/tex]
Put the value of a slope and the coordiantes of the point (-4, 3) or (3, -4) to the equation of a line:
for (-4, 3)
[tex]y-3=-1(x-(-4))\\\\y-3=-(x+4)[/tex]
for (3, -4)
[tex]y-(-4)=-1(x-3)\\\\y+4=-(x-3)[/tex]
