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Three points have coordinates $A (0, 7)$ $B (8, 3)$ and $C (3k, k)$. Find the value of the constant $k$ for which:

i) $C$ lies on the line that passes through $A$ and $B$.

So what I did was that I firstly found the gradient. $y2-y1/x2-x1$. = $m = -1/2$.
Now I write it in the equation: $y = -1/2x + 7$.

The answer mentions that I must replace both the $y$ in the equation, and the $x$ in the equation with $3k$. Why do I have to do this? Why $3k$? I am unable to understand the purpose of why this is being placed in there to complete the question?

Thank you so much!

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1 Answer

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You are solving the system of equations $y=k$, $x=3k$, and $y=-\frac1 2x+7$.

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