write the equation of a line perpendicular to Y=-2X +4 that passes through the point (-1,2)
You want to research and verify the following 2 principles related to perpendicular lines.
The slopes of two perpendicular lines are negative reciprocals.
The product of the slopes of two perpendicular lines is -1 since
-------------
write the equation of a line perpendicular to Y=-2X +4 that passes through the point (-1,2)
The given line is written in "Slope-Intercept" form where y=mx + b....where m=slope and b is intercept....
We need the slope.....or the m portion of the equation so for the line
y=-2x+4.....the slope is m = -2....Right?
Now using the given principles a line perpendicular to this one has a slope that is the negative reciprocal...hmmm
.....let's see....the reciprocal is 1/x....so the reciprocal in this case -1/2......but we are not done yet...
...the slope for a perpendicular line is "negative reciprocal".....so 1/2 is the slope of 2nd line....
....verify.....-2 * 1/2 = -1.......that verifies the 2nd principle above.......
write the equation of a line perpendicular to Y=-2X +4 that passes through the point (-1,2)
....we also want the line to pass through a certain point....that is important because we can use the "point-slope" version of a line to find the equation of the 2nd line....like so.....
y−y1=m(x−x1).......y-2=1/2 (x - (-1))......or y - 2 = 1/2 (x+1)......or y - 2 = 1/2 x + 1/2
....add 2 to both sides......we have.....Y = 1/2 X + 5/2..
..check the point (-1,2)...2 = 1/2 (-1) + 5/2 = 4/2 = 2..it checks perfectly....
so the line Y = - 2 X + 4........IS PERPENDICULAR TO THE LINE.....Y = 1/2 X + 5/2.....Correct?
-------------
You can also graph both of these lines to literally SEE the perpendicular lines cross each other......
