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AQA Maths C1 'lies on the line' question

I'm stuck with the following question 2(c):

I'm unsure on how to get the value of k, here is what my answer looks like (I know its completely wrong)

m=4/3 x=k-2 y=2k-3

y-(2k-3)=4/3(x-(k-2))
y-(2k-3)=4/3x-4/3(k-2)
y=4/3x-4/3k+8/3+2k-3
y=4/3x+2/3k-1/3
3y=4x+2k-1

I think I've used the wrong method would anybody be able to help me with my method so I can find k, and this question please, thanks.

Reply 1

whydoidothis?

just sub them in as x and y into the equation of the line.

(k-2) is the x value and (2k-3) is the y value.

Reply 2

dennisthemenaced

I'm not sure what you did but what I would do would be put x=k-2 and y=2k-3 into the original equation
so ....
4(k-2) - 3(2k-3) = 7
4k -8 -6k +9=7
-2k+1=7
2k=-6
k=-3

Reply 3

Sayless

Thanks, that worked I got the answer now as k=-3