Answer:
[tex]\huge\boxed{y=-\dfrac{5}{2}x-1}[/tex]
Step-by-step explanation:
Parallel lines have the same slope.
The slope-intercept form of an equationo f a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation of the line in a standard form.
Convert to the slope-intercept form:
[tex]5x+2y=12[/tex] subtract 5x from both sides
[tex]2y=-5x+12[/tex] divide both sides by 2
[tex]y=-\dfrac{5}{2}x+6[/tex]
The slope
[tex]m=-\dfrac{5}{2}[/tex]
Therefore we have:
[tex]y=-\dfrac{5}{2}x+b[/tex]
Substitute the coordinates of the given point (-2, 4):
[tex]4=-\dfrac{5}{2}(-2)+b[/tex]
[tex]4=5+b[/tex] subtract 5 from both sides
[tex]-1=b\to b=-1[/tex]
Finally we have:
[tex]y=-\dfrac{5}{2}x-1[/tex]
