Question

What is the equation of the line passing through `(-9,10)` and `(-12,3)`?

Answer 1

We have to first take a locus point on the line denoted by (x,y)

Explanation:

So now the line has three points: `(-9,10)`, `(-12,3)`, and `(x,y)`

Let these points be denoted by A, B, and C respectively.

Now, since AB and BC are line segments lying on the same line, it is obvious that they have equal slope. Hence, we can calculate the slopes for AB and BC separately and equate the slopes to find our required equation.

Slope(AB) = `m1 = (3-10)/(-12-(-9))`
=> `m1=7/3`

Slope(BC)=`m2=(y-3)/(x-(-12))`
=> `m2=(y-3)/(x+12)`

Now,
`m1=m2`
=> `7/3=(y-3)/(x+12)`
=> `7(x+12)=3(y-3)`
=>`7x+84=3y-9`
=>`7x-3y+84-(-9)=0`
=>`7x-3y+93=0`

Which is our required equation!!