SOLUTION: What is the slope of a line parallel and perpendicular to this line? 2�+3y=1

Question 1072408: What is the slope of a line parallel and perpendicular to this line?
2�+3y=1
Found 2 solutions by rothauserc, Theo:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
the point slope form of a line is y = mx + b where m is the slope and b is the y intercept
:
2� + 3y = 1
:
3y = -2x + 1
:
y = -2x/3 + 1/3
:
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The slope of a line parallel to 2�+3y=1 is -2/3
:
The slope of a line perpendicular to 2�+3y=1 is -(1 / (-2/3)) = 3/2
:
Note that the slope of a line perpendicular to another line is the
negative reciprocal of the slope of that line
:
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:

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you have the standard form of the equation, which is ax + by = c

a is the coefficient of x
b is the coefficient of y
c is the constant

you want to convert this to the slope intercept form of y = mx + b

m is the slope
b is the y-intercept.

the conversion works as follows:

start with 2x + 3y = 1

subtract 2x from both sides of the equation to get 3y = 1 - 2x

reorder the terms in descending order of degree to get 3y = -2x + 1

divide both sides of the equation by 3 to get y = -2/3 * x + 1/3

that's the slope intercept form of the equation.

-2/3 is equal to the slope which is equal to m in the general equation.

1/3 is equal to the y-intercept which is equal to b in the general equation.

a line parallel to this line will have the same slope but a different y-intercept.

a line perpendicular to this line will have a slope that is the negative reciprocal of the slope of this line.

we can pick any y-intercept not equal to 1/3 for the parallel line.

we can pick any y-intercept, including 1/3, for the perpendicular line.

the equations i chose to display are:

y = -2/3 * x + 1/3 for the original line

y = -2/3 * x + 5 for the parallel line.

y = 3/2 * x - 10 for the perpendicular line.

the graph of all 3 equations is shown below:

the line of the original equation is blue.
the line of the parallel equation is red.
the line of the perpendicular equation is orange.

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