A graphed line shown shows y=5x-10

Which equation, when graphed with the given equation, will form a system that has no solution?

A. y = - 5x+10

B. y = 5 (x+2)

C. y = 5 (x-2)

D. y = - 5x-10

Option B. y = 5 (x+2)

Step-by-step 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

yeah it is B.

y=5 (x + B)

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