Question

Question #aa9ba

Answer 1

`3y-4x+39=0`

Explanation:

THE POINT SLOPE FORM:-
if a line passes through a point `(a, b)` and has a slope `m` the its equation can be written in point slope form as follows:-
`color(red)(y-b=m(x-a))`

In the given problem;
1. `(a, b) = (9, -1)`
2. `m=4/3`
`therefore` the equation of this line becomes
`y-(-1)=4/3*(x-9)`
`implies 3*(y+1)=4*(x-9)`
`implies 3y+3=4x-36`
`implies color(red)(3y-4x+39=0)` is the required equation

Answer 2

`y+1=4/3(x-9)`

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=4/3" and " (x_1,y_1)=(9,-1)`

`rArry-(-1)=4/3(x-9)`

`rArry+1=4/3(x-9)larrcolor(red)" in point-slope form"`