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
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
Show 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.
Updated On: Jun 26, 2026
- 3
- 2
- -3
- -2
- 0
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
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: Detailed Explanation:
The given equation of the line is \( x - y = 7 \).
The line passes through the point \( (4, a) \).
Substituting \( x = 4 \) and \( y = a \) into the equation:
\[ 4 - a = 7 \]
Solving 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 3: Final Answer:
The value of $a$ is -3.
If a line passes through a given point, the coordinates of that point must satisfy the equation of the line.
Step 2: Detailed Explanation:
The given equation of the line is \( x - y = 7 \).
The line passes through the point \( (4, a) \).
Substituting \( x = 4 \) and \( y = a \) into the equation:
\[ 4 - a = 7 \]
Solving 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 3: Final Answer:
The value of $a$ is -3.
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Straight lines Questions
- Area of the triangle with vertices $(- 2, 2), (1, 5) $and $(6, - 1)$ is
- If a straight line passes through the points $ \left( \frac{-1}{2},1 \right) $ and $(1, 2)$, then its $x$-intercept is
- Let $A (6, -1), B (1, 3)$ and $C (x, 8)$ be three points such that $AB = BC$. The values of $x$ are
- The locus of a point which is equidistant from the points $(1,1)$ and $(3, 3)$ is
- Let $O$ be the origin and $A$ be the point $(64, 0).$ If $P$, $Q$ divide $OA$ in the ratio $1 : 2 : 3$ , then the point $P$ is
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions