Problem

4. Find the value of $\mathrm{k}$ if the line $2 x+k y-9=0$ is parallel to the line $2 x+3 y=1$ ( 2 marks)

Answer

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Answer

Final Answer: The value of \(k\) is \(\boxed{3}\).

Steps

Step 1 ：The slopes of two lines are equal if they are parallel. The slope of a line in the form ax + by = c is -a/b.

Step 2 ：Therefore, the slope of the line \(2x + ky - 9 = 0\) is \(-2/k\) and the slope of the line \(2x + 3y = 1\) is \(-2/3\).

Step 3 ：We can set these two slopes equal to each other and solve for k.

Step 4 ：\(-2/k = -2/3\)

Step 5 ：Solving the equation gives k = 3.

Step 6 ：Final Answer: The value of \(k\) is \(\boxed{3}\).

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