Question

How do you write the equation given (6,-3) with slope 2/3?

Answer 1

Equation of the line is `2x-3y = 21`

Explanation:

The equation of a line passing through `(x_1,y_1)` having slope `m` is `y-y_1= m(x-x_1)`.

Therefore, the equation of a line passing through `(6, -3)` having slope `2/3` is `y-(-3)= 2/3(x-6) or 3(y+3)= 2(x-6) or 2x-3y = 21`.

Equation of the line is `2x-3y = 21` [Ans]

Answer 2

`y=2/3x-7`

Explanation:

The equation of a line in `color(blue)"point-slope form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|))`
where m represents the slope and `(x_1,y_1)" a point on the line"`

`"here " m=2/3" and " (x_1,y_1)=(6,-3)`

`y-(-3)=2/3(x-6)larrcolor(red)" substitute into equation"`

`rArry+3=2/3(x-6)larrcolor(red)" in point-slope form"`

`"distribute / simplify gives an alternative version of equation"`

`y+3=2/3x-4`

`y=2/3x-4-3`

`rArry=2/3x-7larrcolor(red)" in slope-intercept form"`