Question

Through (4, -1) parallel to y=x+2

Answer 1

We will have the following:

We will have that the line that passes through (4, -1) and is parallel tp y = x +2 will be:

First, we remember that the slope of the perpendicular line is given by:

$m_2=-\frac{1}{m_1}$

So:

$m_2=-\frac{1}{1}\Rightarrow m_2=-1$

Now, we replace this information in the general equation of the line:

$y-y_1=m(x-x_1)$

That is:

$\begin{gathered} y-(-1)=-1(x-4)\Rightarrow y+1=-x+4 \\ \\ \Rightarrow y=-x+3 \end{gathered}$

This can be seeing as follows: