Answer:
[tex]\huge\boxed{4x+y=-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]
(x₁, y₁) - point on a line
m - slope
We have
[tex]m=-4,\ (-2,\ 5)\to x_1=-2,\ y_1=5[/tex]
Substitute:
[tex]y-5=-4(x-(-2))\\\\y-5=-4(x+2)[/tex]
Convert to the standard form
[tex]Ax+By=C[/tex]
[tex]y-5=-4(x+2)[/tex] use the distributive property
[tex]y-5=(-4)(x)+(-4)(2)[/tex]
[tex]y-5=-4x-8[/tex] add 5 to both sides
[tex]y-5+5=-4x-8+5[/tex]
[tex]y=-4x-3[/tex] add 4x to both sides
[tex]4x+y=-4x+4x-3\\\\4x+y=-3[/tex]
