Find the value of $k$ , if the line represented by the equation $2 x - k y = 9$ passes through the point $(- 1, - 1)$ .

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Solution

Step 1: Solve for the unknown variable
If the line $2 x - k y = 9$ passes through $(- 1, - 1)$ , Then the point $(- 1, - 1)$ must satisfy the equation $2 x - k y = 9$ .
Substitute $x = - 1 & y = - 1$ in the equation $2 x - k y = 9$ to get:
$\begin{array}{rcl} 2 (- 1) - k (- 1) & = & 9 \\ - 2 + k & = & 9 \\ k & = & 9 + 2 \\ k & = & 11 \end{array}$
Hence, the required value is $k = 11$ .

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