Question

The two lines 2x+3y=7, 8x+12y=1 are____lines

• A. perpendicular
• B. parallel
• C. intersecting
• D. none

Answer 1

The Correct Option is B

To solve the problem, we need to determine the relationship between the two given lines: \(2x + 3y = 7\) and \(8x + 12y = 1\).

1. Convert Each Line to Slope-Intercept Form:
For the general form \(Ax + By = C\), the slope \(m\) is given by:

\( m = -\frac{A}{B} \)

2. Find the Slopes:
For the first line \(2x + 3y = 7\):
\( m_1 = -\frac{2}{3} \)

For the second line \(8x + 12y = 1\):
\( m_2 = -\frac{8}{12} = -\frac{2}{3} \)

3. Compare the Slopes:
Both lines have the same slope \( -\frac{2}{3} \), which means they are parallel.

Final Answer:
The two lines are parallel.