Question

What is the equation of the line passing through `(9,-2)` with slope `m= 2/3`?

Answer 1

`2x-3y-24=0`

Explanation:

The equation of a line passing through two points `(x_1,y_1)` and having a slope `m` is given by

`(y-y_1)=m(x-x_1)`

Given: `x_1=9, y_1=(-2), m=2/3`

Therefore, equation of the line is
`(y-y_1)=m(x-x_1)`
`y-(-2)=2/3(x-9)`
`y+2=2/3(x-9)`

Multiplying both sides by 3,
`3y+6=2x-18`
`2x-3y-24=0`

Answer 2

See explanation.

Explanation:

The slope of the line is given, so the equation is: `y=2/3x+b`.
All we have to do is to calculate the value of `b` for which the given point lies on the line. To do this we have to substitute the coordinates of the point as `x` and `y`:

`-2=2/3*9+b`

If we solve it we get:

`-2=6+b =>b=-8`

Finally we can answer the question:

The line equation is: `y=2/3x-8`.