Question

How do you find the slope of $2y + 3x = - 6$ ?

Answer 1

Hint: In this question, you are given an equation and you have been asked to find the slope. At first, rearrange the terms such that they are in line with the standard form of line. Then, use the formula of slope to find the slope of the given equation of line.

Formula used: 1) Equation of line: $Ax + By + C = 0$
2) Slope = $\dfrac{{ - A}}{B}$

Complete step-by-step solution:
We are given an equation and we have been asked to find the slope. But our given equation is not in the standard form. So, our first step is to rearrange the terms in such a way that the equation is in the same format as of the standard equation.
$ \Rightarrow 2y + 3x = - 6$ …. (given)
But, the standard form of line is $Ax + By + C = 0$.
Rearranging the terms,
$ \Rightarrow 3x + 2y + 6 = 0$
Now, on comparing, we know that –
$A = 3$,
$B = 2$, and
$C = 6$.
We know that the slope of the line is given by $\dfrac{{ - A}}{B}$.
Putting the values in the formula,
$ \Rightarrow $Slope = $\dfrac{{ - 3}}{2}$

Hence, the slope of the equation $2y + 3x = - 6$ is $\dfrac{{ - 3}}{2}$.

Note: There is another equation of line - $y = mx + c$. In this equation, $m$ is the slope.
We will arrange the equation in such a way that it looks in this format. Then, we can identify $m$ as the coefficient of $x$. This $m$ will be our required slope.
$ \Rightarrow 2y + 3x = - 6$ …. (given)
Rearranging the equation by shifting every term to the other side and leaving only the variable $y$.
$ \Rightarrow y = \dfrac{{ - 6 - 3x}}{2}$
Arranging the equation as per $y = mx + c$,
$ \Rightarrow y = \dfrac{{ - 3x}}{2} - 3$
Now, if we notice, the coefficient of $x$ is $\dfrac{{ - 3}}{2}$. This is also the slope of our equation. Hence, our answer is similar to the answer we got using the previous method.