Question

what do the following two equations represent?

• $y + 1 = -4(x - 2)$
• $2x - 8y = 16$

choose 1 answer:
a the same line
b distinct parallel lines
c perpendicular lines
d intersecting, but not perpendicular lines

Explanation:

Step1: Find slope of first line

The first equation is \( y + 1 = -4(x - 2) \). Convert to slope - intercept form (\( y=mx + b \), where \( m \) is slope).
Expand: \( y+1=-4x + 8 \), then \( y=-4x+7 \). So slope \( m_1=-4 \).

Step2: Find slope of second line

The second equation is \( 2x - 8y = 16 \). Solve for \( y \):
Subtract \( 2x \): \( -8y=-2x + 16 \), divide by - 8: \( y=\frac{-2}{-8}x+\frac{16}{-8}=\frac{1}{4}x - 2 \). So slope \( m_2=\frac{1}{4} \).

Step3: Check relationship between slopes

Two lines are perpendicular if \( m_1\times m_2=-1 \).
Calculate \( m_1\times m_2=(-4)\times\frac{1}{4}=-1 \). So the lines are perpendicular.

Answer:

C. Perpendicular lines