Question

How do you write the equation $y-1=-2\left( x-5 \right)$ in slope intercept form?

Answer 1

The given equation $y-1=-2\left( x-5 \right)$ is linear with respect to both of the variables $x$ and $y$. This means that the equation represents a straight line. In the question we have been asked to write the equation in the slope intercept from. The slope intercept form of the line is written in the form of $y=mx+c$. From the slope intercept form, it is clear that we have to separate $y$ on the LHS and express it terms of $x$ in the RHS. Also, we need to separate the variable and the constant terms on the RHS. The coefficient of $x$ in the final equation will be equal to $m$, the slope of the line. And the constant term on the RHS will be equal to $c$, the intercept.

Complete step-by-step answer:
The equation which is given in the question is written as
$y-1=-2\left( x-5 \right).........(i)$
In the question, we are asked to write the above equation in the slope intercept form. We know that the slope intercept form of a line is given by
$y=mx+c.......(ii)$
So we basically need to separate the variable $y$ on the LHS and write it in terms of the variable $x$. For this, we add $1$ on both sides of the equation (i) to get
$\begin{aligned} & \Rightarrow y-1+1=-2\left( x-5 \right)+1 \\\ & \Rightarrow y=-2x+10+1 \\\ & \Rightarrow y=-2x+11.........(iii) \\\ \end{aligned}$
On comparing equations (ii) and (iii) we get the slope and intercept of the given line as $m=-2$ and $c=11$ respectively.
Hence, the equation (iii) represents the required slope intercept form of the given equation.

Note: Do not express $x$ in terms of the variable $y$. From the slope intercept form $y=mx+c$, it is very much clear that we have to write $y$ in terms of $x$. Therefore we need to be familiar with the slope intercept form of a line.