Question:
The equation of the line passing through the points $(1, 2)$ and $(-1, 4)$ is:
The equation of the line passing through the points $(1, 2)$ and $(-1, 4)$ is:
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Always verify the final equation by substituting both points. If both satisfy the equation, it is correct.
Updated On: Jun 16, 2026
- $x + y = 3$
- $x + y = 4$
- $2x + y = 4$
- $x + 2y = 3$
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The Correct Option is A
Solution and Explanation
Concept:
The equation of a straight line passing through two points can be found using slope formula and point-slope form:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}, \quad y - y_1 = m(x - x_1)
\]
Step 1: Find slope Given points: \[ (1,2), \quad (-1,4) \] \[ m = \frac{4 - 2}{-1 - 1} = \frac{2}{-2} = -1 \]
Step 2: Use point-slope form Using point \((1,2)\): \[ y - 2 = -1(x - 1) \] \[ y - 2 = -x + 1 \]
Step 3: Rearrange \[ x + y = 3 \] Thus, the required equation is: \[ \boxed{x + y = 3} \]
Step 1: Find slope Given points: \[ (1,2), \quad (-1,4) \] \[ m = \frac{4 - 2}{-1 - 1} = \frac{2}{-2} = -1 \]
Step 2: Use point-slope form Using point \((1,2)\): \[ y - 2 = -1(x - 1) \] \[ y - 2 = -x + 1 \]
Step 3: Rearrange \[ x + y = 3 \] Thus, the required equation is: \[ \boxed{x + y = 3} \]
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