Question

What is the equation of the line with slope `m= -18/49` that passes through `(4/7, 17/21)`?

Answer 1

`378x+1029y=1049`

Explanation:

Since the slope `m` is defined as
`color(white)("XXX")m=(Delta y)/(Delta x)`

`m=-18/49 = (y-17/21)/(x-4/7)`

After multiplying the right side by `21/21`
`color(white)("XXX")-18/49=(21y-17)/(21x-12)`

Cross multiplying
`color(white)("XXX")(18)(12-21x)=49(21y-17)`

Simplifying:
`color(white)("XXX")216-378x=1029y-833`

`color(white)("XXX")378x+1029y=1049`