Answer:
I and III
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
• Parallel lines have equal slopes
I y = 4x → m = 4
II
y = - [tex]\frac{1}{4}[/tex] x + 2 → m = - [tex]\frac{1}{4}[/tex]
III
rearrange 12x - 3y = 6 into slope- intercept form
subtract 12x from both sides
- 3y = - 12x + 6 ( divide all terms by - 3 )
y = 4x - 2 → m = 4
IV
rearrange into slope- intercept form
4(y + 6) = x - 3
4y + 24 = x - 3 ( subtract 24 from both sides )
4y = x - 27 ( divide all terms by 4 )
y = [tex]\frac{1}{4}[/tex] x - [tex]\frac{27}{4}[/tex] → m = [tex]\frac{1}{4}[/tex]
I and II have the same slope, hence are parallel lines
