Question

Given the linear equation \(y = 2x + k\), determine the value of k if the point P(3, 7) lies on the line.

• A. 1
• B. 3
• C. 0
• D. 2

Hint:

Simply substitute the given coordinates directly:
\(y - 2x = k \implies 7 - 2(3) = k \implies k = 1\).
Rearranging the equation before substitution makes the arithmetic very clear.

Answer 1

The Correct Option is A

Step 1: Rearrange the line's equation to isolate k first.
Starting from $y = 2x + k$, we can write \[ k = y - 2x \] This tells us that for any point lying on this line, k is just whatever is left after subtracting twice the x-coordinate from the y-coordinate.
Step 2: Plug in the coordinates of P(3, 7). \[ k = 7 - 2(3) = 7 - 6 \]
Step 3: Conclude. \[ k = 1 \] \[ \boxed{k = 1} \]