Answer:
Options1 and 2.
Step-by-step explanation:
Firstly, we need to change the third and fourth choices to y=:
6x + 3y = 18
Subtract 6x from both sides:
6x + 3y - 2x = 18 - 6x
3y = 18 - 6x
Divide both sides by 3:
[tex]\frac{3y}{3} = \frac{18}{3} - \frac{6x}{3}[/tex]
y = 6 - 2x
y = -2x + 6
Fourth choice:
4y - 8x = 6
Add 8x to both sides:
4y - 8x + 8x = 6 + 8x
4y = 6 + 8x
Divide both sides by 4:
[tex]\frac{4y}{4} = \frac{6}{4} + \frac{8x}{4}[/tex]
y = [tex]\frac{3}{2}[/tex] + 2x
y = 2x + [tex]\frac{3}{2}[/tex]
Now, two lines are perpendicular when their slopes are multiplied together to create a negative number. The different slopes are:
Option 1: 1/2
Option 2: 1/2
Option 3: -2
Option 4: 2
So this means that option 1 is perpendicular to option 3 (1/2 * -2 = -1) and option 2 is also perpendicular to option 3 with the same calculation.
So, the two correct answers are options 1 and 2.
Hope this helps!
