Find the value of $p$ , if the lines $y = 3 x + 7$ and $y + p x = 3$ are parallel to each other.

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Solution

Finding the value of $p$ :
The general equation of a line is given by :
$y = m x + b$
Here , the $m$ is the slope
Given that the Lines $y = 3 x + 7$ and $y + p x = 3$ are parallel to each other.
When two lines are parallel then their slopes are always equal
$⇒ m_{1} = m_{2}$
The slope of line $y = 3 x + 7$ is $3$
The slope of line $y = - p x + 3$ is $- p$
Being parallel the slopes of both the given equations $y = 3 x + 7$ and $y + p x = 3$ must be equal
$\Rightarrow p = - 3$
Therefore, the value of $p$ is $- 3$

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