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

Hint: 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.