Question

1. $y - 4 = -8(x + 1)$

a) $y = -x - 4$
c) $y = -4x - 1$
b) $y = 8x - 4$
d) $y = -8x - 4$

1. $y + 4 = -(x - 4)$

a) $y = 1$
b) $y = x$
c) $y = -x$
d) $y = x + 1$

Explanation:

Problem 9

Step1: Expand the right side

We have the equation \( y - 4 = -8(x + 1) \). First, we expand the right - hand side using the distributive property \( a(b + c)=ab+ac \). Here, \( a=-8 \), \( b = x \) and \( c = 1 \), so \( -8(x + 1)=-8x-8\times1=-8x - 8 \). The equation becomes \( y-4=-8x - 8 \).

Step2: Solve for y

To solve for \( y \), we add 4 to both sides of the equation \( y-4=-8x - 8 \). Using the addition property of equality (if \( a=b \), then \( a + c=b + c \)), we get \( y=-8x-8 + 4 \).

Step3: Simplify the right side

Simplify \( -8x-8 + 4 \). Combine the constant terms: \( -8 + 4=-4 \). So \( y=-8x-4 \).

Step1: Expand the right side

We have the equation \( y + 4=-(x - 4) \). Expand the right - hand side using the distributive property \( -(a - b)=-a + b \). Here, \( a=x \) and \( b = 4 \), so \( -(x - 4)=-x+4 \). The equation becomes \( y + 4=-x + 4 \).

Step2: Solve for y

To solve for \( y \), we subtract 4 from both sides of the equation \( y + 4=-x + 4 \). Using the subtraction property of equality (if \( a=b \), then \( a - c=b - c \)), we get \( y=-x+4 - 4 \).

Step3: Simplify the right side

Simplify \( -x+4 - 4 \). The \( 4-4 = 0 \), so \( y=-x \).

Answer:

D) \( y = -8x - 4 \)

Problem 10