Question

Determine if the lines are parallel, perpendicular, neither or the same line: 3x + 2y = 1 and y = -x - 1.

the same line or
perpendicular

Answer 1

neither

Explanation:

Parallel lines have equal slopes

The product of the slopes of perpendicular lines equals - 1

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

3x + 2y = 1 ( subtract 3x from both sides )

2y = - 3x + 1 ( divide each term by 2 )

y = -
`(3)/(2)` x +
`(1)/(2)` ← in slope- intercept form

with slope m = -
`(3)/(2)`

y = - x - 1 ← is in slope- intercept form

with slope m = - 1

Since the slopes are not equal then the lines are not parallel

-
`(3)/(2)` × - 1 =
`(3)/(2)` ≠ - 1

Then the lines are not perpendicular

Answer 2

Neither

Explanation:

When you rearrange the equation 3x+2y=1 in the form of y=mx+c

you get:

2y=-3x+1

`y=-(3)/(2) x+0.5`

And if you compare it with the equation y= -x -1

You can see that the gradient is not the same, so it means it is not parallel.

To get if it is perpendicular you need to see if the two gradients multiply to give the value -1 but when you multiply

`-(3)/(2)`×
`-1= 3/2` so it is not perpendicular as well

I hope it is right, feel free to point out anything wrong or you're unsure of :)