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Find the equation of a line passing through the points (-1,1) and (2,-4)

Answer» Let the given points be A(-1,1) and (2,-4) .
We know that the equation of a line passing through the points.
`(x_(1),y_(1)) and (x_(2),y_(2))"is given by"((y-y_(1)))/((x-x_(1)))=((y_(2)-y_(1)))/((x_(2)-x_(1)))`
Here, `x_(1)=-1, y_(1)=1, x_(2)=2 and y_(2)=-4`.
So, the equation of a line passing through the given points is
`((y-1))/(x-(-1))=((-4-1))/(2-(-1)) Leftrightarrow ((y-1))/((x+1))=(-5)/(3)`
`Leftrightarrow 3(y-1)=-5(x+1)`
`Leftrightarrow 5x+3+2=0`.
Hence, the required equation is 5x+3y+2=0.


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