[tex]\Large\textsc{Answer\::}[/tex]
[tex]\Large\textsc{\textbf{Calculations\::}}[/tex]
First , notice that the equation of the second line , 6x=3y+5 , is not written in the same form as y=2x , so determining the slope is hard .
To determine the slope , we need to convert the first equation into slope intercept form .
Subtract 6x on both sides :
0 = 3y+5-6x
Now , subtract 3y on both sides :
-3y=-6x+5
Divide by -3 on both sides :
y=-6/-3x+5/-3
Which simplifies to :
y=2x-5/3 (remember , a negative divided by a negative results in a positive)
Put both equations together :
y=2x and y=2x-5/3
Notice that the slopes are the same . This indicates that the lines are parallel .
Now let's focus on the second maths problem :
Consider the equations below .
x=-4 and y=-2
Are the lines parallel or perpendicular?
The slope of the first line is undefined , and the slope of the second line is zero .
Lines with undefined slopes are vertical , and lines with slopes of zero are horizontal .
Here's something you may have recalled from your Geometry class :
Is a vertical line parallel or perpendicular to a horizontal line ?
The ans is : perpendicular .
[tex]\footnotesize{\texttt{hope helpful~}[/tex]