Question

Find the equation of the line below. ​

Answer 1

A.
`y= - (1)/(3) x`

Explanation:

Line is passing through the point
`(3,\:-1)=(x_1, \:y_1)` and origin
`(0,\: 0)=(x_2, \: y_2)`

Equation of line in two point form is given as :

`\frac {y-y_1}{y_1 - y_2} = (x-x_1)/(x_1 - x_2) \\\\</p><p>\therefore (y-(-1))/(-1-0)= (x-3)/(3-0)\\\\</p><p>\therefore (y+1)/(-1)= (x-3)/(3) \\\\</p><p>\therefore 3(y+1) = - 1(x-3)\\\\</p><p>\therefore 3y + 3 = - x +3\\\\</p><p>\therefore 3y = - x +3-3\\\\</p><p>\therefore 3y = - x\\\\</p><p>\huge \orange {\boxed {\therefore y= - (1)/(3) x}}`

Answer 2

Option A. is the right choice.

Explanation:

y-intercept is 0, and slope is negative.

`\mathrm{Slope\:}\left(0,\:0\right),\:\left(3,\:-1\right):\\\\\quad m=(-1-0)/(3-0)=-(1)/(3)`

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