What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4)? y = – 5/2x – 1y = –5/2 x + 5y = 2/5x – 1y = 2/5x + 5

First find the slope of the given line like this:
[tex]5x + 2y = 12\\2y=-5x+12\\y=\frac{-5}{2}x+6[/tex]
If two lines are parallel, then they have the same slope, so the equation we are looking for is in the form:
[tex]y=\frac{-5}{2}x+a[/tex] and we have to find b using the given point like this:
Substitute x = -2 and y=4 in the above equation like this and solve for a:
[tex]4=\frac{-5}{2}(-2)+a[/tex] 
[tex]4=5+a[/tex] 
[tex]a=4-5=-1[/tex] 
The equation of the line is then the following:
[tex]y=\frac{-5}{2}x-1.[/tex]