Question

The graphs of the equations \( 2x + 3y + 15 = 0 \) and \( 3x - 2y - 12 = 0 \) are which type of straight lines?

• A. Coincident straight lines
• B. Parallel straight lines
• C. Intersecting straight lines
• D. None of these

Hint:

Two straight lines are intersecting if their slopes are not equal.

Answer 1

The Correct Option is C

We have the two equations: 1) \( 2x + 3y + 15 = 0 \) 2) \( 3x - 2y - 12 = 0 \) To determine the relationship between these lines, we compare the slopes of the two lines. The slope of a line \( ax + by + c = 0 \) is given by \( \text{slope} = -\frac{a}{b} \). For the first line, \( 2x + 3y + 15 = 0 \), the slope is: \[ \text{slope}_1 = -\frac{2}{3}. \] For the second line, \( 3x - 2y - 12 = 0 \), the slope is: \[ \text{slope}_2 = -\frac{3}{-2} = \frac{3}{2}. \] Since the slopes are not equal, the lines are not parallel. Therefore, they are intersecting straight lines. Thus, the correct answer is \( \boxed{\text{Intersecting straight lines}} \).