First slide

Equation of line in Straight lines

Question

If the lines $y = 2 x + 3$ , $y = 3 x + 4$ and $y = mx + 7$ are concurrent then m=

Easy

A

6
B

-37
C

37
D

-27

Solution

Three lines are said to be concurrent, if those three lines are passing through the same point.
To get the point of intersection of two lines $y = 2 x + 3$ , $y = 3 x + 4$
Equate both equations
$\begin{matrix} 2 x + 3 = 3 x + 4 \\ x = - 1 \end{matrix}$
Substitute x=-1 , in the equation $y = 3 x + 4$
$\begin{matrix} y = 3 (- 1) + 4 \\ = 1 \end{matrix}$
The point of intersection is $(- 1, 1)$
Since three lines are concurrent, the point $(- 1, 1)$ lies on the line $y = mx + 7$
Hence,
$\begin{matrix} 1 = - m + 7 \\ m = 6 \end{matrix}$
Therefore, $m = 6$

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