Answer: Second option.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
It is important to remember the following:
1- The slopes of parallel lines are equal.
2- The slopes of perpendicular lines are negative reciprocal.
Then, given the first equation:
[tex]y= -2x+4[/tex]
You can identify that:
[tex]m=-2[/tex]
The second equation is:
[tex]-5x+10y=5[/tex]
Solve for "y":
[tex]10y=5x+5\\\\y=\frac{5}{10}x+\frac{5}{10}\\\\y=\frac{1}{2}x+\frac{1}{2}[/tex]
You can identify that:
[tex]m=\frac{1}{2}[/tex]
Then, since the slopes are negative reciprocal, you can conclude that the lines for the given pair of equations are perpendicular.
