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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

User Rocksyne
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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


User Yuming Cao
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6.8k points
4 votes

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.

consider the line 6x-2y=-8. what is the slope of a line perpendicular to this line-example-1
User BrentM
by
8.6k points

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