Parallel lines are line that have same slope, where m1 = m2. To identify what line are parallel to each other, convert the equation into y=mx+b and get the slope of each equation.

Line 1, y=mx+b

y=0x-5 , where the slope of line 1 is m1=0

Line 2, y=mx+b

4y−16x=−1 , simplifying the equation by multiplying it by \(\displaystyle\frac{{1}}{{4}}\) will result to \(\displaystyle{y}={4}{x}-\frac{{1}}{{4}}\), where the slope of the line 2 is m2=4

Line 3, x=-6 , since the graph of the line 3 is vertical its slope is undefined.

Line 4, y=mx+b

y+5=4(x+1) y=4x-4 , where the slope of line 4 is also m4=4. Therefore, based on the slopes of the given equations, we can say that line 2 and line 4 is parallel to each other.

Line 1, y=mx+b

y=0x-5 , where the slope of line 1 is m1=0

Line 2, y=mx+b

4y−16x=−1 , simplifying the equation by multiplying it by \(\displaystyle\frac{{1}}{{4}}\) will result to \(\displaystyle{y}={4}{x}-\frac{{1}}{{4}}\), where the slope of the line 2 is m2=4

Line 3, x=-6 , since the graph of the line 3 is vertical its slope is undefined.

Line 4, y=mx+b

y+5=4(x+1) y=4x-4 , where the slope of line 4 is also m4=4. Therefore, based on the slopes of the given equations, we can say that line 2 and line 4 is parallel to each other.