The Equation of the Line with Slope −3/2 and Which is Concurrent with the Lines 4x + 3y − 7 = 0 and 8x + 5y − 1 = 0 is - Mathematics

MCQ

The equation of the line with slope −3/2 and which is concurrent with the lines 4x + 3y − 7 = 0 and 8x + 5y − 1 = 0 is

Options

•  3x + 2y − 63 = 0

•  3x + 2y − 2 = 0

• 2y − 3x − 2 = 0

• none of these

Solution

3x + 2y − 2 = 0

Given:
4x + 3y − 7 = 0      ... (1)
8x + 5y − 1 = 0      ... (2)
The equation of the line with slope $- \frac{3}{2}$ is given below: $y = - \frac{3}{2}x + c$ $\Rightarrow \frac{3}{2}x + y - c = 0$          ... (3)
The lines (1), (2) and (3) are concurrent.

$\therefore \begin{vmatrix}4 & 3 & - 7 \\ 8 & 5 & - 1 \\ \frac{3}{2} & 1 & - c\end{vmatrix} = 0$

$\Rightarrow 4\left( - 5c + 1 \right) - 3\left( - 8c + \frac{3}{2} \right) - 7\left( 8 - \frac{15}{2} \right) = 0$

$\Rightarrow - 20c + 4 + 24c - \frac{9}{2} - 56 + \frac{105}{2} = 0$

$\Rightarrow \frac{- 40c + 8 + 48c - 9 - 112 + 105}{2} = 0$

$\Rightarrow 8c = 8$

$\Rightarrow c = 1$

On substituting c = 1 in $y = - \frac{3}{2}x + c$, we get:

$y = - \frac{3}{2}x + 1$

$\Rightarrow 3x + 2y - 2 = 0$

Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Q 30 | Page 135