Question

What is the equation of the line with slope `m= 1/6` that passes through `(-5/12,4/3)`?

Answer 1

`12x-72y+101=0.`

Explanation:

If a line with slope `m` passes thro. pt. `(x_1,y_1)`, its eqn. is given by, : `y-y_1=m(x-x_1).`

Using this, we can write the desired eqn. as `y-4/3=1/6(x+5/12),` or, `(3y-4)=1/2(x+5/12),` i.e., `24(3y-4)=12x+5.`
`:. 12x+5-72y+96=0,` i.e., `12x-72y+101=0.`