Question

What is the equation of the line with slope `m=-4` that passes through `(4,5)`?

Answer 1

`4x+y-21=0`

Explanation:

Using point gradient formula:

`(y-y_1)=m(x-x_1)`
where `(x_1,y_1)` is `(4,5)`

`(y-5)=-4(x-4)`
`y-5=-4x+16`
`4x+y-21=0`

Answer 2

`y=-4x+21`

Explanation:

`m=-4` is equivalent to the gradient by `y=mx+c`. The coordinates `(5,4)` indicates that the point occurs when `x=5` and `y=4` and these are free variables that you can plug in for `x` and `y`.

Using the format of `y=mx+c` solve for `c`:

`y=mx+c`
`5=-4(4)+c`
`5=-16+c`
`5+16=c`
`c=21`

Therefore, the equation for the slope is:

`y=-4x+21`

Answer 3

Equation of the line is `4 x + y =21`

Explanation:

The equation of line passing through `(x_1=4,y_1=5)` having

slope of `m=-4` is `y-y_1=m(x-x_1) ;`

`:. y-5= -4 (x-4) or y-5 = -4 x +16` or

`4 x + y =21 ;`

Equation of the line is `4 x + y =21 ;` [Ans]