Question:
Which of the following represents the slope of the line passing through points (3, −2) and
(3, 4)?
Which of the following represents the slope of the line passing through points (3, −2) and
(3, 4)?
Show Hint
If two points have the same \(x\)-coordinate, the line is vertical and its slope is undefined. If two points have the same \(y\)-coordinate, the line is horizontal and its slope is \(0\).
Updated On: Jun 6, 2026
- \(0\)
- \(1\)
- \(-\dfrac{3}{2}\)
- ∞
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The Correct Option is D
Solution and Explanation
Concept:
The slope of a straight line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by: \[ m=\frac{y_2-y_1}{x_2-x_1} \]
Step 1: Identify the given points.
The given points are: \[ (3,-2) \] and \[ (3,4) \] So, \[ x_1=3,\quad y_1=-2 \] and \[ x_2=3,\quad y_2=4 \]
Step 2: Apply the slope formula. \[ m=\frac{4-(-2)}{3-3} \] \[ m=\frac{4+2}{0} \] \[ m=\frac{6}{0} \]
Step 3: Interpret the result.
Division by zero is not defined. Therefore, the slope of the line is undefined.
Step 4: Geometrical meaning.
Since both points have the same \(x\)-coordinate, the line is vertical. \[ x=3 \] A vertical line has an undefined slope. \[ \therefore \text{The slope is undefined.} \]
The slope of a straight line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by: \[ m=\frac{y_2-y_1}{x_2-x_1} \]
Step 1: Identify the given points.
The given points are: \[ (3,-2) \] and \[ (3,4) \] So, \[ x_1=3,\quad y_1=-2 \] and \[ x_2=3,\quad y_2=4 \]
Step 2: Apply the slope formula. \[ m=\frac{4-(-2)}{3-3} \] \[ m=\frac{4+2}{0} \] \[ m=\frac{6}{0} \]
Step 3: Interpret the result.
Division by zero is not defined. Therefore, the slope of the line is undefined.
Step 4: Geometrical meaning.
Since both points have the same \(x\)-coordinate, the line is vertical. \[ x=3 \] A vertical line has an undefined slope. \[ \therefore \text{The slope is undefined.} \]
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