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: Understanding the Question:
This question is from Coordinate Geometry and Linear Equations.
We are given a line equation with an unknown constant \(k\). We are also given a point that lies on this line, and we need to solve for \(k\).

Step 2: Key Formula or Approach:
If a point \(P(x_1, y_1)\) lies on a line represented by an equation, the coordinates of the point must satisfy the equation when substituted.

Step 3: Detailed Explanation:
The given equation of the line is:
\[ y = 2x + k \]
The point lies on this line is:
\[ P(x, y) = (3, 7) \]
This means we can substitute:
\[ x = 3, \quad y = 7 \]
Substitute these coordinates into the equation:
\[ 7 = 2(3) + k \]
Calculate the product:
\[ 7 = 6 + k \]
Isolate \(k\) by subtracting 6 from both sides:
\[ k = 7 - 6 \]
\[ k = 1 \]

Step 4: Final Answer:
The value of \(k\) is \(1\).