Answer: [tex]y=-\frac{5}{2}x-1[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
Write the equation of the given line in Slope-Intercept form by solving for "y":
[tex]5x + 2y = 12\\\\2y=-5x+12\\\\y=-\frac{5}{2}x+6[/tex]
You can observe that the slope of this line is:
[tex]m=-\frac{5}{2}[/tex]
Since the slopes of parallel lines are equal, then the slope of the other line is:
[tex]m=-\frac{5}{2}[/tex]
Now, substitute the slope and the point (-2, 4) into [tex]y=mx+b[/tex] and solve for "b":
[tex]4=-\frac{5}{2}(-2)+b\\\\4=\frac{10}{2}+b\\\\4-5=b\\\\b=-1[/tex]
Then the equation of the line parallel to the given line is:
[tex]y=-\frac{5}{2}x-1[/tex]
