How do I write an equation to a line that is perpendicular to an equation?

Question

For example, I need to write an equation to a line that is perpendicular to 2x + 3y = 6.

I don't need the exact answer, as much as I need a complete and hopefully simple explanation as to how to carry out this problem. I really appreciate your help!!!

Answer 1

find the slope, m, of your line (-2/3 in this case).

The slope of any perpendicular line will be -1/m (3/2 in this case).

So for any real number b,
. . . . . . . y = (-1/m)x + b = (3/2)x + b
is the equation of a line perpendicular to the original line.

Answer 2

First, convert the line into the form y = mx + b first

You know that m is slope and b is the y-intercept.
You know that the product of slopes of 2 perpendicular lines is -1.(you can find proof in different places!)

So if m is the slope of one line, then the other is the negative reciprocal of it.
Examples,
The slope of a line perp. to a line w/ slope of 7 is -1/7.
The slope of a line perp. to a line w/ slope of -2/3 is 3/2.

You then create a new line y = mx + b, with m as the new slope and b as any real number(because you said that you only want to find the equation of a perpendicular and not where the intersection will be)
so
If I have a line 2x + 3y = 6, convert it first into y = mx + b
2x + 3y = 6
3y = -2x + 6
y = -2/3 x + 2

The negative reciprocal of -2/3 is 3/2, so the possible perpendiculars are:
y = 3/2 x + 5
y = 3/2 x + 6
y = 3/2 x + 1/2
y = 3/2 x - 6
y = 3/2 x
y = 3/2 x - pi
y = 3/2 x + sqrt 5

As you know, there is an infinite number of perpendiculars for every line.
^_^

Answer 3

First, re-write the equation in y= mx + b form:
Re- Written: 3y = -2x + 6
simplified: y = -2/3x + 2

The slope of the first line is then -2/3. Therefore, the slope of the other line must be +3/2 because the slope of a line perpendicular to another is always the negative reciprocal.

Now you have: y = 3/2x + b
Because it is to be a perpendicular line, the number representing b must be the same in both equations because that is where the lines will meet on the y axis.
That is why the answer becomes:
Original equation: y = -2/3x + 6
Perpendicular Equation: y = 3/2x + 6

Answer 4

first we need to get The in this form of y = mx + b where m = slope of the line

so 2x + 3y = 6 is same as 3y = -2x + 6 which is same as
y= -2/3x + 2 so the slope of this line is -2/3 the slope of a perpendicular line is opposite reciprocal so it is 3/2 so any mine of form y = 3/2x + b is perpendicular to that line b can be any number

Answer 5

There are several ways to figure the orthaganol line.

One simple way:

Write the equation in slope/intercept format:

3y=-2x+6
y=-2/3 x +6

A line with the same intercept and opposite slope would necessarily be perpendicular to the original line, so:

y= 3/2 x + 6 should work

Answer 6

Perpendicular means 90 degrees (but you know that)

One of forms for an equations of a straight line is y=mx + b where m is a slope and b is the y-axis intercept. (you probably knew that too)

m=tan(delta y/delta x) this is just for kicks.


Now rotate a line by 90 degrees which is the same as changing the angle = atan(m) to angle + 90 or angle in radians + pi/2. Then go and get the new slop for the perpendicular line. m=tan(angle + 90).

Case in point
y = mx + b the perpendicular line then is y =- mx + b

Start with 2x + 3y = 6 to make it into y=-2x/3 +2 and the rest is cake

Have fun

Answer 7

Create an equation that has a slope that is the negative inverse of the original equation. For example, in the given equation, the slope is -2/3, so the slope of your perpindicular line should be 3/2.

Answer 8

2x + 3y = 6
3y = -2x + 6
y = (-2/3)x + 2

The line that is perpendicular to y = (-2/3)x + 2, would have a slope of (3/2), so

y = (3/2)x + b

now lets say they have a coordinate in common

y = (-2/3)x + 2
y = (-2/3)(6) + 2
y = (-12/3) + 2
y = -4 + 2
y = -2

Using (6,-2)

y = (3/2)x + b
-2 = (3/2)(6) + b
-2 = (18/2) + b
-2 = 9 + b
-11 = b

so now you have y = (3/2)x - 11

y = (3/2)x - 11
2y = 3x - 22
-3x + 2y = -22

so now you have

2x + 3y = 6
-3x + 2y = -22

For which the 2 lines are perpendicular at (6,-2)

Answer 9

First you must format your equation to the form y=mx+b, in which m is the slope, and b the y-intercept.

you can do this to your equation and you will get:

y=-2/3x+2

the slope of a perpindicular line needs to have the negative reciprocal of the slope of the original equation.

the negative reciprocal of -2/3 is 3/2. The slope of the perpindicular line must have a slope of 3/2

Answer 10

For the given equation, determine your slope. Then write a new equation with the slope being the oposite reciprocal of the slope in your first equation. Keep the same Y-intercept.

Ex.

y=2x+1


y= -1/2x+1


If you graph this you will see tht the lines are perpendiular!!