Agraphed 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

i believe it is c.y = 9x

rise over run. 9 units up over 1 unit right or 9/1