Question

consider the line 6x-2y=-8. what is the slope of a line perpendicular to this line. what is a slope of a line parallel to this

Answer 1

Answers

Part 1: y = (-1/3)x + 4

(this is one of the lines perpendicular to 6x-2y=-8 that pass through point (0, 4))

Part 2

3

Step-by-step explanation

This question has two parts.

Part 1

You want to get the line equation of a line perpendicular to 6x-2y=-8. Since you have given the point on that line, I will assume you want any of the line perpendicular to it.

Let's take that the perpendicular line will pass through a point on the line 6x-2y=-8.

When x= 0

2y= 6x + 8

y = 3x + 4

y = (6×0 + 8)

=4

Thus,

a point (0, 4) and the gradient is (-1/3)

Gradient = Δy/Δx

-1/3= (y-4)/(x-0)

-1(x)=3(y-4)

-x = 3y - 12

3y = -x +12

y = (-1/3)x + 4

Part 2

Parallel lines have the same slope.

The slope of 6x-2y=-8 is 3.

6x-2y=-8

2y= 6x + 8

y = 3x + 4

slope = 3

Answer 2

When you solve for y, the coefficient of x is the slope of the line and of any that are parallel to it.

... -2y = -6x -8

... y = 3x +4

The slope of a parallel line is 3.

_____

The slope of a perpendicular line is the negative reciprocal of the slope of the given line.

The slope of a perpendicular line is -1/3.