Question

Which of the following lines is NOT parallel toy = 3x + 4?

Answer 1

We are to look for lines that are not parallel to y=3x + 4

Comparing the above equation with y=mx + b, the slope(m) = 3

Equations of lines are said to be parallel, if they have the same slope

So, we need to re-write each equation in the slope-intercept form to see which is NOT parallel to the given equation

OPTION A

3y - 9x - 6 = 0

`y=(9x)/(3)+(6)/(3)`
`y=3x+2`

slope = 3 which implies. it is parallel to the given equation

OPTION B

-2y + 6x + 4 = 0

`2y=6x+4`

Divide through by 2

`y=3x\text{ + 2}`

slope = 3 which implies the line is parallel to the given line

OPTION C

2y - 6x - 4 = 0

`2y=6x\text{ + 4}`

Divide through the equation by 2

`y=3x\text{ + 2}`

slope = 3 which implies the line is parallel to the given line

OPTION D

2y - 4x - 8 = 0

`2y=4x\text{ + 8}`

Divide through the equation by 2

`y=2x\text{ + 4}`

slope = 2, which means tthe line is NOT parallel to the given line.

Therefore, the line which is NOT parallel to y=3x+ 4 is D. 2y - 4x - 8 = 0