Question

Consider the line - 6x-2y = -5.What is the slope of a line perpendicular to this line?What is the slope of a line parallel to this line?Slope of a perpendicular line: 1X?Slope of a parallel line:0

Answer 1

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

`\begin{gathered} (-2y)/(-2)=(6x)/(-2)-(5)/(-2) \\ y=-3x+2.5 \end{gathered}`

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