equation of lines. -x+y=4 is perpendicular to what?

Question

my book said that -x+y=4 is perpendicular to x+y-2....how did this happen? can you explain to me how to get the perpendicular line of a certain equation of line

Answer 1

two lines are perpendicular if the slope of the first line is the negative reciprocal of the slope of the second line and vice versa.

1st line: -x + y = 4 or we can write this in the form

y= x + 4

slope = 1

2nd line: x + y = 2
or
y = -x + 2

slope = -1

the slopes as you can see are the negative reciprocal of each other. Thus we can definitely say that they are perpendicular.

Answer 2

Two lines are perpendicular if the slope of the first line is the negative reciprocal of the slope of the second line and the other way around.

We have - x + y = 4

Solving for y we get:

y = x + 4

The slope here is 1.

What is the negative reciprocal of 1?

Well, -1, right?

The second equation is x + y = -2

Isolating y we get:

y = - x - 2

The slope here is -1. The exact slope we found in the other equation.

Since the slope of the first equation = the slope of the second equation, the two given lines are perpendicular.

Answer 3

Both of your linear equations are in 'standard form' ... that is ...
Ax + By = C, where A,B and C are numbers, and x and y are the two variables.

The slope of a line in standard form is -(A/B), and the slope of any line perpendicular to it would have slope B/A (called a negative reciprocal)

So, in your example, the slope of -x+y=4 is -(-1/1), which is 1. And the slope of the other equation, x+y=2 is -(1/1), which is -1.

Since the two slopes are negative reciprocals of each other, they are, in fact, perpendicular.

Answer 4

Lines are perpendicular if their slopes are reciprocals.

i.e. slope of x= 1/2
reciprocal of x= 2/1

Answer 5

Right and Up becomes DownRight awesome.
So remember RightUp goes to DownRight.
Or RightUp goes to UpRight.
Either way it works, no sorry it doesn't.
RightUp goes to DownRight.
Or DownLeft goes to LeftUp.

Now learn about rise and run, which makes slope.
Learn about the -1/m, where m is slope.

It's all very visual if you learn to graph it on graph paper.

Like y = 15x.
I'll give it away and ruin the learning.
y = mx.
So m = 15, which is slope.
But who cares.

Learn on your own.
Get out some graph paper and guess
numbers that make the equation work out right.
Plot the points with right and up amounts.
Draw a perpendicular and figure out how things are similar and different.

Answer 6

y = x + 4 has slope (gradient) of 1
Perpendicular line will have slope - 1
Equation of perpendicular line is:-
y = - x + C
This is as far as we can go unless we are given a point that this line passes thro`.
eg if line passes thro` (0,2):-
2 = 0 + C
C = 2
y = - x + 2
x + y - 2 = 0