Answer:
Option B. y = 5(x+2)
Explanation:
we have
y=5x-10
The slope of the given line is m=5
Remember that
If two lines are parallel, then their slopes are the same
If a system of linear equations has no solutions, then the lines of the system must be parallel lines with different y-intercept
Verify each case
case A) y=-5x+10
The slope of this line is m=-5
The slopes are different
therefore
This equation, when graphed with the given equation, will form a system that has one solution
case B) y=5(x+2)
y=5x+10
The slope of this equation is the same of the given equation and their y-intercepts are different
therefore
The system has no solutions
case C) y=5(x-2)
y=5x-10
This equation is the same of the given equation
therefore
The system has infinitely solutions
case D) y=-5x-10
The slope of this line is m=-5
The slopes are different
therefore
This equation, when graphed with the given equation, will form a system that has one solution