Question

How do you write $5x+y=-3$ into slope – intercept form?

Answer 1

We know that the slope – intercept of any straight line is as follows: $y=mx+c$. In this form, “m” is the slope of the straight line and “c” is the intercept of the line. So, in order to write the given equation $5x+y=-3$ in slope – intercept form, we have to arrange this equation of a straight line in such a manner so that we will get this equation of the following form: $y=mx+c$.

Complete step by step solution:
The equation given in the above problem which we have to write in slope – intercept form is as follows:
$5x+y=-3$
As the equation given above is a straight line so we are going to rearrange the above equation in this slope – intercept form.
And we know that the slope – intercept form for straight line is as follows:
$y=mx+c$
In the above equation, “m” is the slope and “c” is the intercept.
Subtracting 5x on both the sides of the given equation we get,
$\begin{aligned} & \Rightarrow 5x+y=-3 \\\ & \Rightarrow y=-3-5x \\\ \end{aligned}$
Now, again rearranging the above equation in the form of $y=mx+c$ and we get,
$\Rightarrow y=-5x-3$
Comparing the above equation in the form of $y=mx+c$ we get,
Then “m” is -5 which is the slope and -3 is the y – intercept (or “c”) of the straight line.
Hence, we have written the slope – intercept form of the given straight line as follows: $y=-5x-3$.

Note:
The mistake that could be possible in the above problem is that you might forget to write the sign of the slope given above. The slope – intercept form which we have written above is as follows:
$y=-5x-3$
Now, you might have a tendency to write the slope of this straight line as 5 and forgot to put the negative sign so make sure you should incorporate the negative sign.