Which equation is equivalent to y - 6 = -12(x + 4)
A. Y = -6x - 48
B. Y = 6x - 48
C. Y = -6x - 42
D. Y = -12x - 54
To make the given equation y - 6 = -12(x + 4) equivalent to one of the options with y on one side, we have to simplify and solve for y. Let's do that:
y - 6 = -12(x + 4)
Distribute the -12 to both x and +4:
y - 6 = -12x - 48
Now add 6 to both sides to isolate y:
y = -12x - 48 + 6
Simplify by combining like terms:
y = -12x - 42
This gives us the equation that represents y in terms of x. Comparing this to the options provided:
A. y = -6x - 48 (Incorrect as the coefficient of x is -12 and not -6)
B. y = 6x - 48 (Incorrect as the sign on the coefficient of x should be negative)
C. y = -6x - 42 (Incorrect as the coefficient of x should be -12 and not -6)
D. y = -12x - 54 (Incorrect as the constant term should be -42 and not -54)
It looks like there's a mistake because none of the provided options match the correct equation, which is y = -12x - 42. However, it's possible that the intended correct answer is close to Option C, which has the correct constant term but the incorrect coefficient for x.