Question

Find the length of the intercept made by the line $ x + 1 = 0 $ between the lines: $$ 3x + 2y = 5 \quad \text{and} \quad 3x + 2y = 3 $$

• A. 2
• B. 1
• C. 3
• D. 4

Hint:

To find intercept length between two lines on a given line, substitute the given constraint into both equations to get intersection points.

Answer 1

The Correct Option is B

We are to find the length of the segment of the line \( x + 1 = 0 \) (i.e., vertical line \( x = -1 \)) between two other lines. Substitute \( x = -1 \) into both lines: First line: \[ 3(-1) + 2y = 5 \Rightarrow -3 + 2y = 5 \Rightarrow 2y = 8 \Rightarrow y = 4 \] Second line: \[ 3(-1) + 2y = 3 \Rightarrow -3 + 2y = 3 \Rightarrow 2y = 6 \Rightarrow y = 3 \] So the points of intersection are:
- \( A = (-1, 4) \)
- \( B = (-1, 3) \) These lie on a vertical line, so: \[ \text{Length of intercept} = |4 - 3| = \boxed{1} \]