Question

Tell whether the lines for each pair of equations are parallel,perpendicular,or neither,

y= -2x+4
-5x+10y=5

Answer 1

Answer: Second option.

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

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:

`y= -2x+4`

You can identify that:

`m=-2`

The second equation is:

`-5x+10y=5`

Solve for "y":

`10y=5x+5\\\\y=(5)/(10)x+(5)/(10)\\\\y=(1)/(2)x+(1)/(2)`

You can identify that:

`m=(1)/(2)`

Then, since the slopes are negative reciprocal, you can conclude that the lines for the given pair of equations are perpendicular.