Point (3, 4) lies on the graph of the equation 3y = kx + 7. The value of k is

Question

Point (3, 4) lies on the graph of the equation 3y = kx + 7. The value of k is

1. A. 4/5
2. B. 5/3 (Correct answer)
3. C. 4/3
4. D. 4/7

Correct Answer

Option B — 5/3

Detailed Solution & Explanation

The correct answer is 5/3.

Key Points

• If a point lies on the graph of an equation, its coordinates must satisfy that equation.
• Substituting $x = 3$ and $y = 4$ into $3y = kx + 7$:
  • $3(4) = k(3) + 7$
  • $12 = 3k + 7$
  • $3k = 5$
  • $k = \frac{5}{3}$

Additional Information

• This substitution principle is the whole of the topic. Three question types follow from it:
  • Given a point and the equation, find the unknown coefficient (as here).
  • Given the equation and one coordinate, find the other coordinate.
  • Given a point and an equation, verify whether the point lies on the line.
• Verification: with $k = \frac{5}{3}$, the equation is $3y = \frac{5}{3}x + 7$. At $x = 3$: $3y = 5 + 7 = 12$, so $y = 4$. ✓
• Always substitute back — it costs a few seconds and catches every arithmetic slip.