Question

How do you write the equation $-3x-6y=-24$ in slope intercept form?

Answer 1

We are given an equation in two variables, namely $x$ and $y$. We have written this given equation in the slope – intercept form, which is, $y=mx+c$ and where ‘m’ is the slope, ‘c’ is the y – intercept. So, we will rearrange the given equation by carrying out suitable operations and will make it look similar to the slope – intercept form.

Complete step by step answer:
According to the question given to us, we are given an equation with two variables, namely $x$ and $y$. We have write this given equation in the slope – intercept form, which is,
$y=mx+c$
where ‘m’ is the slope and ‘c’ is the y – intercept.
The given equation we have is,
$-3x-6y=-24$----(1)
We have to write the equation (1) in terms of $y$. We will first take the negative charge out as common, we get,
$\Rightarrow 3x+6y=24$---(2)
Now, we will divide the equation (2) by 3, we get,
$\Rightarrow \dfrac{3x}{3}+\dfrac{6y}{3}=\dfrac{24}{3}$
$\Rightarrow x+2y=8$----(3)
Now, we will subtract equation (3) by $x$ and we get,
$\Rightarrow x+2y-x=8-x$
Solving further, we get,
$\Rightarrow 2y=8-x$----(4)
Now, we will divide equation (4) by 2, and we get,
$\Rightarrow \dfrac{2y}{2}=\dfrac{1}{2}(8-x)$
The expression we get on solving further,
$\Rightarrow y=\dfrac{8}{2}-\dfrac{x}{2}$
Rearranging the above expression in the slope intercept form, we have,
$\Rightarrow y=-\dfrac{x}{2}+4$
Or
$\Rightarrow y=-\dfrac{1}{2}x+4$

Therefore, the slope intercept form of the given equation is $y=-\dfrac{1}{2}x+4$.

Note: The slope – intercept form of the given equation that we obtained can be interpreted as,
$y=-\dfrac{1}{2}x+4$
Here, the slope of the line made using the equation $y=-\dfrac{1}{2}x+4$ is $-\dfrac{1}{2}$.
Y – intercept here will be $4$ and that point will be $(0,4)$. Y-intercept refers to the point when the line of an equation intersects the y – axis and x is 0 at that point.