MATH QUESTION!? Please help!!?

Question

" Write the equation of a line that passes through (3, -1) and is perpendicular to 3x + 2y = 7"

Does anyone know the formula to find this??? Or how to find what the perpendicular equation is????

PLEASE HELP!

Answer 1

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2 + 2 = 4

you wolcome

Answer 2

Perpendicular lines have slopes that are negative reciprocals. So since 3x + 2y = 7 has a slope of -3/2 then the slope of the line you are looking for has a slope of 2/3.

m = 2/3

You are given that it passes through (3,-1), therefore, since

y = mx + b, you substitute in to get,

-1 = (2/3)*3 + b which implies b = -3

So, m = 2/3 and b = -3 therefore, the equation of the line is

y = (2/3)x - 3

Answer 3

first, solve the equation for y

3x + 2y = 7

2y = -3x + 7

y = -3/2x + 7/2

next, find the slope of the perpendicular line.

We know that m(1) = -3/2

The rule is m(1) = -1/m(2)  m(2) is the slope of the perpendicular line

so, if m(1) = -3/2, m(2) is the negative reciprocal, ie. 2/3

so, now we now the slope is 2/3 (m), we can use the points given to work out the equation of the line.

y - y(1) = m { x - x(1)}

y - -1  = 2/3 ( x - 3)

y + 1 = 2/3 x - 2

y = 2/3 x -3

ta da!

now that we have the slope

Answer 4

First put the equation into mx + b form to find the slope.

This give us y = -(3/2)x + (7/2)

A line perpindicular to this will have the negative reciprocal slope.  Thus the slope of the line you're looking for will be (2/3).

Then since we know it passes through (3, -1) we can set up an equation with the slope we know now.  This equation will look like this:

-1 = (2/3)(3) + b.  Solving for b, we get b = -3.  

Putting that altogether the equation of the line that passes through (-3, 1) and is perpindicular to 3x + 2y = 7 is y = (2/3)x - 3.

Answer 5

first step: 3x+2y=7

therefore: 2y=7-3x

therefore: y= -(3/2)x + (7/2)

therefore the gradient of this line is: -(3/2)

second step: let this gradient = m1  and let the gradient of the unknown line = m2

since m2= -(1/m1)  (this is a learned formula)

therefore, m2= (2/3)  (just substitute m1 into the above formula)

step thee: using the point gradient formula: (y-y1)/(x-x1)=m put the given point (3, -1) into this learned formula where y1= (-1) and x1= (3)

eg.  (y-(-1)/(x-(3)=m  (where m= (2/3))

now use cross multiplication to get: 3y+3=2x-6

now rearrange the equation a little to get: 3y = 2x-9

now divide both sides by "3" to get: y= (2/3)x -3

and that is the unknown line's formula: y=(2/3)x -3

in general form this formula is: 2x-3y-9 = 0

i hope this helps

Answer 6

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