Question

given the equations y = 4x + 5 and y = 4x - 7, what is the relationship?
a. both
b. perpendicular
c. neither
d. parallel

Explanation:

Step1: Recall line - slope relationship

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For the line $y = 4x+5$, the slope $m_1 = 4$. For the line $y = 4x - 7$, the slope $m_2 = 4$.

Step2: Determine relationship

Two lines are parallel if their slopes are equal ($m_1=m_2$), perpendicular if $m_1\times m_2=- 1$. Since $m_1 = m_2=4$, the lines are parallel.

Answer:

D. Parallel