Question

Write the standard form of the equation of the line through the given point with the given slope. Through (-2,5), slope =-4

Answer 1

Answer:

$\huge\boxed{4x+y=-3}$

Step-by-step explanation:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

(x₁, y₁) - point on a line

m - slope

We have

$m=-4,\ (-2,\ 5)\to x_1=-2,\ y_1=5$

Substitute:

$y-5=-4(x-(-2))\\\\y-5=-4(x+2)$

Convert to the standard form

$Ax+By=C$

$y-5=-4(x+2)$                 use the distributive property

$y-5=(-4)(x)+(-4)(2)$

$y-5=-4x-8$               add 5 to both sides

$y-5+5=-4x-8+5$

$y=-4x-3$               add 4x to both sides

$4x+y=-4x+4x-3\\\\4x+y=-3$