Question

What is the equation of the line with slope `m= -1/8` that passes through `(7,-3)`?

Answer 1

`x+8y=-17`

Explanation:

`y=mx+c`
or
`-3=-7/8+c`
or
`c=-3+7/8`
or
`c=-(24+7)/8`
or
`c=-17/8`
So the equation is
`y=-x/8-17/8`
or
`8y=-x-17`
or
`x+8y=-17`

Answer 2

`y=-1/8x-17/8`

Explanation:

The equation of a line in `color(blue)"point-slope form"` is

`color(red)(|bar(ul(color(white)(a/a)color(black)(y-y_1=m(x-x_1))color(white)(a/a)|)))`
where m represents the slope and `(x_1,y_1)" a point on the line"`

here `m=-1/8" and " (x_1,y_1)=(7,-3)`

substitute these values into the equation.

`y-(-3)=-1/8(x-7)`

`rArry+3=-1/8x+7/8rArry=-1/8x+7/8-3`

`rArry=-1/8x-17/8" is the equation of the line"`