Given the line - 6x-2y = -5
Write the given equation of the line in the form y = mx + c
where m is the slope
- 6x-2y = -5
Add 6x to both sides
-2y = 6x -5
Divide both sides by -2
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{6x}{-2}-\frac{5}{-2} \\ y=-3x+2.5 \end{gathered}[/tex]
Comapring this with y=mx + c
m = -3
This means the slope of the line - 6x-2y = -5 is -3
a.
Note that when two lines are perpendicular to each other, the product of thier slopes is -1
Let n represents the slope of the line perpendicular to line - 6x-2y = -5
It implies -3 x n = -1
-3n = -1
n=-1/-3
n = 1/3
Hence, the slope of a line perpendicular to the line -6x-2y = -5 is 1/3
b.
Note that if two lines are parallel to each other, they have equal slopes.
Hence, the slope of a line parallel to the line - 6x-2y = -5 is -3
