Question

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.

Answer 1

1 neither

2 neither

3 neither

Explanation:

Answer 2

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.