Can someone help please I am so confused?

Question

I have learned to wait until the last min to do my homework and i am totally lost.

Find the equation, in standard form, with all inter coefficients, of the line perpendicular to x+ 3y =6 and passing through (-3, 5). Show all work

Answer 1

x + 3y = 6

First, put that equation in slope-intercept form (y = mx + b)

3y = -x + 6
y = (-1/3)x + 2

All lines that are perpendicular to the given line have a slope that is the negative reciprocal (flip the fraction and change the sign).

So, the slope of the given line is -1/3
the slope of a perpendicular line is +3/1 or 3.

So, now you have the slope (m = 3) and a point (-3, 5).

Use point-slope form...
when you have a slope (m) and a point (a, b):
y - b = m(x - a)

y - 5 = (3)(x - -3)
y - 5 = (3)(x + 3)
y - 5 = 3x + 9
y = 3x + 14
-3x + y = 14
3x - y = -14

Answer 2

..I've gotten a different answer than everyone here, but maybe this makes sense.

You'd first change that equation to standard by dividing each side by three(I've noticed everyone elses turning out negative, and there's no reason for it. The new coefficient needs to be positive):

y=(1/3)x+6.

Then switch the slope so that it's perpendicular(uses opposite reciprocal, -3):

y=(-3)x+6.

Now, find the y-intercept of the new line by plugging in the coordinate given:

(5)=(-3)(-3)+b.
b=-4.

Now just plug everything and make sure you've got the right form. You're new equation is:

y=(-3)x-4.

Answer 3

Convert x+3y=6 to standard linear form y= -x/3+2.
The slope of this line is -1/3.
A line perpendicular to this line has a reciprocal slope.
The reciprocal of 1/3 is 3.
The new line will have the linear equation y=3x+b which is all the lines perpendicular to y= -3/x+2.
But you just want the line through ( -3,5) so substitute in y=3x+b
to find b.
5= 3( -3)+b or b=14
Answer is y=3x+14.

The two lines intersect at ( -3.6, 3.2).

Answer 4

Put the line in standard form:

y = -(1/3)x + 6

A line perpendicular to this has slope of -inverse of the slope above, namely 3.

Find the appropriate intercept by using the point given:

y = 3x + b,

5 + 9 = 14 = b

so the line is y = 3x + 14

Answer 5

the original equation rewritten in slope-intercept form is
y= -(1/3)x+2

the slope is -(1/3)

to be perpendicular the slope must be the negative reciprocal (flip the fraction and change sign)

so, the new slope is 3

y-y1=m(x-x1) point slope form of a line

so

y-5=3(x-(-5))

y-5=3(x+5)

y-5+3x+15

y=3x+20

Answer 6

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Answer 7

ok, the line perp to

3y = - x + 6
y = - 1/3 x + 2

should be

y = 3x + c

that's due to eq y = mx + c with slopes (-1 / 3)(3) = -1

Answer 8

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Answer 9

you have to do homework during the summer that must suck sorry i can't help you though

Answer 10

sounds like you need to unlearn that bad habit and get started sooner. good luck