Question

this question has two parts. first, answer part a, then answer part b.
part a
correct!
2 out of 2 points.
consider the graphs of the following equations.
y = -2x 2y = x 4y = 2x + 4
a. which equations are parallel? explain your reasoning.
2y = x and 4y = 2x + 4 are parallel because they have the same slope
part b
incorrect
1 try left. try once more
b. which equations are perpendicular? explain your reasoning.
y = -2x and 2y = x are perpendicular because they have the same slope
select choice are perpendicular because they have select choice

Explanation:

Step1: Find slopes of each equation

For \( y = -2x \), slope \( m_1 = -2 \) (in \( y = mx + b \) form).
For \( 2y = x \), rewrite as \( y=\frac{1}{2}x \), slope \( m_2=\frac{1}{2} \).
For \( 4y = 2x + 4 \), rewrite as \( y=\frac{2}{4}x + 1=\frac{1}{2}x + 1 \), slope \( m_3=\frac{1}{2} \).

Step2: Check perpendicular slopes

Two lines are perpendicular if \( m_1 \times m_2 = -1 \).
Check \( m_1=-2 \) and \( m_2=\frac{1}{2} \): \( (-2)\times\frac{1}{2}=-1 \).
So \( y = -2x \) (slope -2) and \( 2y = x \) (slope \( \frac{1}{2} \)) are perpendicular because their slopes multiply to -1.

Answer:

\( y = -2x \) and \( 2y = x \) are perpendicular because they have slopes that multiply to -1.