Question

Can you help me with this assignment

Answer 1

The two lines are said to be parallel if thier slopes are equal

where, the slope of a line is express as:

`\begin{gathered} y\text{ =m(x-a)+b} \\ \text{ m is the slope} \end{gathered}`

The given expression of line : y= -2x - 1

On comparing with the general equation of line, slope is

m = (-2)

A) x + 2y =-10

Simplify the general equation of line

x+2y =-10

2y=-10-x

y= -x/2 -5

Here slope is (-1/2)

So, the lines are not parallel

B) 2x-y=4

Simplify in the general equation of line

2x-y=4

y=2x-4

Here slope is 2

So, the lines are not parallel.

C)2y-x=-6

Simplify in the general equation of line

2y - x = -6

2y = x - 6

y = x/2 - 3

Here slope is 1/2

So, the lines are not parallel.

D) 2x + y =-6

Simplify in the general equation of line

2x + y =-6

y = -6 -2x

y = -2x -6

Here slope = (-2)

So, the lines are parallel.

The equation 2x + y =-6 & y= -2x - 1 have slope = (-2)

So, the lines are parallel

Answer : D) 2x + y =-6