Question

How do you find the slope of $4y - 2x = - 16$?

Answer 1

In this question, we need to find the slope of the given straight line. Firstly, we will convert the given equation into a slope intercept form of a straight line. It can be done by first adding $2x$ for both sides of the given equation. Then dividing each term by 4 and rearranging the obtained equation. We then compare the given equation of a line with the standard slope intercept form of a line and find the required slope.

Complete step-by-step answer:
Given the equation of a straight line $4y - 2x = - 16$ …… (1)
We are asked to find out the slope of the line given in the equation (1).
To find this, we need to convert our given equation into slope intercept form of a straight line.
The general equation of a straight line in slope intercept form is given by,
$y = mx + c$ …… (2)
where $m$ is the slope or gradient of a line and $c$ is the intercept of a line.
Now we convert the given equation of a line into slope intercept form by rearranging the terms.
Consider the equation of a line given in the equation (1).
Adding $2x$ on both sides of the equation (1), we get,
$\Rightarrow 4y - 2x + 2x = - 16 + 2x$
Combining the like terms $- 2x + 2x = 0$
Hence we get,
$\Rightarrow 4y + 0 = - 16 + 2x$
$\Rightarrow 4y = - 16 + 2x$
Now dividing throughout by 4 we get,
$\Rightarrow \dfrac{{4y}}{4} = \dfrac{{ - 16 + 2x}}{4}$
$\Rightarrow y = \dfrac{{ - 16}}{4} - + \dfrac{2}{4}x$
Rearranging the above equation we get,
$\Rightarrow y = \dfrac{2}{4}x - \dfrac{{16}}{4}$
Simplifying further, we get,
$\Rightarrow y = \dfrac{1}{2}x - 4$ …… (3)
Comparing with the standard slope intercept form given in the equation (2), we get,
$m = \dfrac{1}{2}$ and $c = - 4$.
Which is the slope and y-intercept of the given straight line.
Hence we can conclude that the slope of the straight line $4y - 2x = - 16$ is $m = \dfrac{1}{2}$.

Note:
In this question, it is important to remember that $y = mx + c$ is the form called the slope intercept form of the equation of the straight line. It is the most popular form of the straight line.
Sometimes the given equation of a line won’t be the same as the general form. We need to convert or make rearrangement in the given expression such that it becomes similar to the general slope intercept form. So then, it becomes easier to find the required things.