Question

How do you find the slope of the line perpendicular to $4x + 2y = 10$?

Answer 1

This problem deals with finding the value of the slope of the line perpendicular to the given line. Here in order to find the value of the slope perpendicular to the given line, first we find the slope of the given line as we know that the product of slopes of any two perpendicular lines is equal to -1.
$\Rightarrow {m_1}{m_2} = - 1$

Complete step-by-step solution:
Given a linear equation in two variables which is $4x + 2y = 10$
The slope of the equation is equal to $m$, and the constant $c$ is the intercept.
Now considering the given equation as shown below: $y = mx + c$
$\Rightarrow 4x + 2y = 10$
Now transferring the term $4x$ to the right hand side of the above equation as shown below:
$\Rightarrow 2y = 10 - 4x$
Now dividing the above equation by the number 2 as shown below:
$\Rightarrow y = - 2x + 5$
So here the slope of the equation $y = - 2x + 5$ is given by:
$\Rightarrow m = - 2$
Now the slope of the equation which is perpendicular to the $y = - 2x + 5$ is given by $\dfrac{{ - 1}}{m}$.
Here we know that $m = - 2$, now finding the value of the expression $\dfrac{{ - 1}}{m}$ as shown below:
$\Rightarrow \dfrac{{ - 1}}{m} = \dfrac{{ - 1}}{{ - 2}}$
$\Rightarrow \dfrac{{ - 1}}{m} = \dfrac{1}{2}$
Hence the slope of the line perpendicular to $4x + 2y = 10$ is equal to $\dfrac{1}{2}$.
The slope of the line perpendicular to the line $4x + 2y = 10$ is equal to $\dfrac{1}{2}$.

Note: Please note that the above problem is done by first finding the slope of the above given line and then from the obtained slope value, finding the value of the slope of line perpendicular to it. Most important point to remember is that two lines which are parallel have the same slope, whereas the lines which are perpendicular have their product of slopes to be -1.