For what value of k does the line represented by the equation 1-kx = -3y contain the point (4,-3)?

k=-2

 

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8)

1 - kx  =  -3y

 

If this line passes through the point  (4, -3) , then we know that  x = 4  and  y = -3  are solutions to the equation. We know that this is true...

 

1 - k(4)  =  -3(-3)     Now solve this for  k .

1 - 4k  =  9

-4k  =  8

k  =  -2

Substitute the point (4,-3) into the equation 1-kx = -3y

(Note: Why can we do this? Because when a point lies on a line, if you sub the x coordinate into all 'x's in the equation and y coordinate into all 'y's in the equation, then you will get left hand side equals right hand side.)

1 - 4k = -3(-3)

1 - 4k = 9

4k = 1 - 9 = -8

k = -8/4 = -2