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

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

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`