Question

What is the equation of the line with slope `m= -7/6` that passes through `(-7/12,2/3)`?

Answer 1

`84x+72y=-1`

Explanation:

Using the definition of slope:
`color(white)("XXX")m=(Delta y)/(Delta x)`
and given values:
`color(white)("XXX")`slope: `m=-7/6`,
`color(white)("XXX")`a point: `(-7/12,2/3)`,
and using a variable point `(x,y)` on the required line:

`color(white)("XXX")-7/6=(y-2/3)/(x-(-7/12))`

Multiplying the right side by `12/12` to clear the fractions:
`color(white)("XXX")-7/6 = (12y-8)/(12x+7)`

Then multiply both sides by `6(12x+7)` to clear the denominators
`color(white)("XXX")-7(12x+7)=6(12y-8)`

Simplify
`color(white)("XXX")-84x-49=72y-48`

Add `(84x+48)` to both sides (and flip the sides to write in standard form)
`color(white)("XXX")84x+72y=-1`