What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?y = x + 4y = x + y = –5x + 4y = –5x +

The given blue line passes through points (0, -3) and (-5, -4). This means that its slope m is 

[tex]\displaystyle{ m= \frac{y_2-y_1}{x_2-x_1}=\frac{-3-(-4)}{0-(-5)}= \frac{-3+4}{5}= \frac{1}{5} [/tex].

Any line parallel to this line has the same slope, that is 1/5.


The equation of the line with slope 1/5, passing through the point (-2, 2) is:

             [tex]y-2= \frac{1}{5}(x-(-2))\\\\y-2= \frac{1}{5}x+ \frac{2}{5} [/tex]. 


Adding 2 to both sides, we have: 
 
                    [tex]y= \frac{1}{5}x +\frac{12}{5} [/tex].


Answer: [tex]y= \frac{1}{5}x +\frac{12}{5} [/tex].