Question

How do you express $2x+y=8$ in the form $y=mx+b$, what is the slope and y intercept?

Answer 1

Hint: The equation of the line given in the above question is written as $2x+y=8$. To write it in the form of $y=mx+b$, we have to separate the variable y on the LHS and write it in terms of the variable x on the RHS. So we have to subtract $2x$ from both the sides of the given equation $2x+y=8$ so that the given equation will reduce in the form of $y=mx+b$. Since $y=mx+b$ is the slope intercept form, where $m$ is the slope and $b$ is the y-intercept, on comparing the obtained equation with $y=mx+b$, we will get the respective values of the slope and the y intercept.

Complete step-by-step solution:
The equation given in the above question is
$\Rightarrow 2x+y=8$
For writing the above equation in the form of $y=mx+b$, we subtract $2x$ from both the sides to get
$\begin{align}
  & \Rightarrow 2x+y-2x=8-2x \\
 & \Rightarrow y=-2x+8 \\
\end{align}$
On comparing the above equation with the slope intercept form $y=mx+b$, we get the respective values of the slope and the y intercept as
$\Rightarrow m=-2$
And
$\Rightarrow b=8$
Hence, the given equation is written in the form of $y=mx+b$ as $y=-2x+8$ and the slope and the y intercept are $-2$ and $8$ respectively.

Note: We can also use the differentiation method to get the value of the slope. For this, we have to differentiate the both sides of the equation $2x+y=8$ with respect to x, and the value of the derivative $\dfrac{dy}{dx}$ will be equal to that of the slope. And for getting the value of the y intercept, we can put $x=0$ in the given equation from which the obtained value of y will be equal to the y intercept.