Answer: y = 3x + 13
Explanation:
Rearrange the equation to slope-intercept form:
[tex]6x - 2y + 10 = 0\\\\-2y=-6x-10\\\\y=(-\frac{1}{2} )(-6x-10)\\\\y=3x+5 \left \{ {{slope=3} \atop {y-intercept=5}} \right.[/tex]
A parallel line shares the same slope:
[tex]y=3x+b[/tex]
Substitute in the given point to find the y-intercept(b):
[tex]y=3x+b\\\\7=3(-2)+b\\\\7=-6+b\\\\b=7+6=13[/tex]
Therefore, the equation of the parallel line is:
[tex]y=3x+13\\[/tex]
