Verified answer

Any two parallel lines always have the same slope. First we need to find the slope of given line.

2x-4 = y  (slope intercept form  y=mx+b)

slope(m) = 2

Now we have slope m=2 and point(-3,-11) to find new line.

y=2x+b

Plugin x=-3 and y=-11  to get b value

-11=2(-3)+b

-11+6 =b

-5=b

So new line parallel to given line would have the equation as,

y= mx+b

y=2x-5

:-

m = 2

y + 11 = 2 ( x + 3 )

y + 11 = 2x + 6

y = 2x - 5

Slop of the line = 2 as it is parallel to 2x-y =4.

Equation, (y+11) = 2(x+3),

y = 2x - 5.

Lines parallel to 2x-y=4 are of the form 2x-y=C for some real constant C.

If 2x-y=C passes through (-3, -11) then C = 2(-3)-(-11) = 5.

The equation of a line that passes through the point (-3,-11) and is parallel to the line whose equation is 2x-y=4 is 2x-y=5.  ← ← ← ANSWER

In general, the line parallel to ax+by=c through a given point (x₀,y₀) is ax+by = ax₀+by₀. 

2(-3) - ( - 11) =  5 ===> 2x - y = 5

Lines that are parallel will have the same coefficients for their variables.

2x - y = C

We know that when x = -3 , y = -11

2 * (-3) - (-11) = C

-6 + 11 = C

5 = C

2x - y = 5

That's it.