Question

How do you write the equation of the line that is parallel to $y = x + 3$ and passes through $(-4, 1)$?

Answer 1

Hint: We will first write the general equation which is equal to $y = x + 3$, then we will put the point $(- 4, 1)$ in the general equation and get the required values.

Complete step-by-step solution:
We are given that we are required to write the equation of the line that is parallel to $y = x + 3$ and passes through $(- 4, 1)$.
Now, since the line is parallel to $y = x + 3$, therefore, it must be of the type $y = x + c$ where $c$ is the intercept.
Now, since we are also given that the line passes through $(- 4, 1)$, therefore putting $x = - 4 $ and $y = 1$ must satisfy the equation $y = x + c.$
Therefore, putting $x = - 4$ and $y = 1$ in the equation “$y = x + c$”, we will then obtain the following equation:-
$ \Rightarrow $ $1 = (- 4) + c$
Removing the bracket from right hand side of the above equation, we will then obtain the following equation:-
$ \Rightarrow $ $1 = - 4 + c$
Re – arranging the terms in the above equation, we will then obtain the following equation:-
$ \Rightarrow $ $c = 5$

Hence, the required equation is $y = x + 5$.

Note: The students must note that we know that a general equation of line is given by “$y = mx + c$”, where m is the slope of the line.
Now, since we were given that the line we have to find is parallel to $y = x + 3$ which has the slope as $1$.
Therefore, the required line also has the slope of 1 and thus we have the equation of line in the form of “$y = x + c$”.