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HELP !! The equations of three lines are given below.

Line 1: 10x - 6y=8
Line 2: 3y = 5x +7
Line 3: y=5/3x -8
For each pair of lines, determine whether they are parallel, perpendicular, or neither.

HELP !! The equations of three lines are given below. Line 1: 10x - 6y=8 Line 2: 3y-example-1
User Khadisha
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2 Answers

2 votes

Answer:

1 neither

2 neither

3 neither

Explanation:

User Sureshkumar Menon
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4.4k points
2 votes

All three lines are parallel to each other.

To determine whether two lines are parallel, perpendicular, or neither, we can examine the slopes of the lines.

The general form of a linear equation is , where
y = mx + b where is the slope and b is the y-intercept.

Let's compare the slopes of the given lines:

Line 1:
10x - 6y = 8
Rewrite it in slope-intercept form
(y = mx + b):10x - 6y = 8


-6y = -10x + 8


y = 5/3x - 4/3

The slope of Line 1 is m₁ = 5/3.

Line 2:
3y = 5x + 7

Rewrite it in slope-intercept form
(y = mx + b):3y = 5x + 7


y = (5)/(3)x + (7)/(3)

The slope of Line 2 is m₂ = 5/3.

Line 3:
y = 5/3x - 8

The slope of Line 3 is m₃ = 5/3.

Since m₁ = m₂, Lines 1 and 2 are parallel.
Since m₁ = m₃, Lines 1 and 3 are parallel.
Therefore, Lines 1, 2, and 3 are all parallel to each other.

User Niiru
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