Question

What is the equation of the line with slope `m= -1/4` that passes through `(7,13)`?

Answer 1

`y=-1/4x+59/4`

Explanation:

Make use of the point-slope form `y-y_1=m(x-x_1)` where `m` is the slope and `x_1` and `y_1` are the `x` and `y` values of the given point.

`[1]" "y-y_1=m(x-x_1)`

Substitute the values of `m`, `x_1`, and `y_1`.

`[2]" "y-(13)=(-1/4)[x-(7)]`

Distribute `-1/4` to `(x-7)`.

`[3]" "y-13=-1/4x+7/4`

Add `13` to both sides.

`[4]" "y-13+13=-1/4x+7/4+13`

`[5]" "y=-1/4x+7/4+13`

Add `7/4` and `13`.

`[6]" "y=-1/4x+7/4+52/4`

`[7]" "color(blue)(y=-1/4x+59/4)`