Question

How do you write the equation in point slope form given (–2, 15), (9, –18)?

Answer 1

`y-15=-3(x+2)`

Explanation:

Slope:
`color(white)("XXX")m=(Delta y)/(Delta x) = (15-(-18))/(-2-9)=33/(-11) = -3`

The general slope-point form for a line with slope `m` through a point `(barx,bary)` is
`color(white)("XXX")y-bary=m(x-barx)`

Using `(-2,15)` for `(barx,bary)`
`color(white)("XXX")y-15=-3(x+2)`

Answer 2

Equation of the line is `3x+y=9`

Explanation:

Equation of the line between two points say `(x_1,y_1)` and `(x_2,y_2)` in point slope form is given by

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`, where both LHS and RHS represent slope of the line,

Hence equation of the line between `(-2,15)` and `(9,-18)` is given by

`(y-15)/(x-(-2))=((-18)-15)/(9-(-2))` i.e.

`(y-15)/(x+2)=(-18-15)/(9+2)` or `(y-15)/(x+2)=(-33)/11=-3` i.e.

`(y-15)=-3*(x+2)` i.e.

`(y-15)=--3x-6`

or `3x+y=-6+15=9`

As such, equation of the line is `3x+y=9`