Question

What is the equation of the following line written in slope-intercept form?

(-5, -1)
Oy=3/2x-13/3
Oy=-2/3x-13/3
Oy=2/3x-13/3​

Answer 1

Option (2)

Explanation:

Let the equation of the line is,

y - y' = m(x - x')

where (x', y') is a point lying on the given line.

And m = slope of the line =
`(y_2-y_1)/(x_2-x_1)`

Line given in the graph passes through two points (-5, -1) and (-2, -3).

Slope of the line 'm' =
`(-3+1)/(-2+5)`

=
`-(2)/(3)`

Therefore, equation of the line passing through(-5, -1) and slope of the line =
`-(2)/(3)` will be,

y - (-1) =
`-(2)/(3)[x-(-5)]`

`y+1=-(2)/(3)(x+5)`

`y=-(2)/(3)x-(10)/(3)-1`

`y=-(2)/(3)x-(13)/(3)`

Option (2) will be the answer.