Question

1. circle one: parallel, perpendicular, neither

3x + 9y = 18
3x + 9y = 27

Explanation:

Step1: Convert equations to slope - intercept form ($y = mx + b$)

For the first equation $3x + 9y=18$:
Subtract $3x$ from both sides: $9y=-3x + 18$.
Divide by $9$: $y=-\frac{3}{9}x+\frac{18}{9}$, so $y =-\frac{1}{3}x + 2$.
For the second equation $3x + 9y=27$:
Subtract $3x$ from both sides: $9y=-3x + 27$.
Divide by $9$: $y=-\frac{3}{9}x+\frac{27}{9}$, so $y =-\frac{1}{3}x + 3$.

Step2: Compare slopes ($m$ values)

The slope of the first line is $m_1=-\frac{1}{3}$.
The slope of the second line is $m_2=-\frac{1}{3}$.
Since $m_1 = m_2$ (and the $y$-intercepts $b_1 = 2$ and $b_2=3$ are different), the lines are parallel.

Answer:

Parallel