Question

If the equation of the straight line passing through the points $(3, -4)$ and $(4, a)$ is $x - y = 7$, then the value of $a$ is equal to

• A. 3
• B. 2
• C. -3
• D. -2
• E. 0

Hint:

When a point $(x, y)$ is on a line, simply plug the values into the equation. There is no need to calculate the slope or use the two-point form if the equation is already provided.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
If a line passes through a given point, the coordinates of that point must satisfy the equation of the line.
Step 2: Key Formula or Approach:
Substitute \(x = 4\) and \(y = a\) directly into the equation \(x - y = 7\) and solve for \(a\).
Step 3: Detailed Explanation:
The given equation is:
\[ x - y = 7 \] We know the point \((4, a)\) lies on this line.
Substitute \(x = 4\) and \(y = a\):
\[ 4 - a = 7 \] Solve for \(a\):
\[ -a = 7 - 4 \] \[ -a = 3 \] \[ a = -3 \] (We can verify with the other point \((3, -4)\): \(3 - (-4) = 3 + 4 = 7\), which is correct.)
Step 4: Final Answer:
The value of \(a\) is -3.