A quick fraction question about line slope

[mklangelo]

Hello to all!

This is my first post to the Math Forum.

I am a 52 year old man who has decided to refresh myself in math. Many moons ago I struggled for a C in Algebra 101 in College.

I'd like to do better as I think Math is a great way to discipline the mind.

Any way, here is my question. I am graphing equations and figuring slopes etc...

If I have an equation of this line: Y=(-1/3X) - (- 1/2) I know my Y intercept is (-1/2) but with the Slope, It shows as: Negative 1/3 But in the final reduction/simplification shows as Negative 1 divided by Positive 3

How did that negative sign get legally moved from referring to the whole fraction to now just the Numerator?

Thanks in advance.

Mk

[Guest]

This is incorrect:

Y intercept is (-1/2)

Y intercepts OY at 1/2
becase
the equation of line is:
Y=(-1/3X) - (- 1/2)

Y = -1/3x + 1/2

when x=0, y=1/2

[mklangelo]

This is incorrect:

Y intercept is (-1/2)

Y intercepts OY at 1/2
becase
the equation of line is:
Y=(-1/3X) - (- 1/2)

Y = -1/3x + 1/2

when x=0, y=1/2

-1 is what I did not distribute on y-intercept.

[Guest]

I am not same Guest as above...Ill call myself GuestWho....

Mkl....Your question and answer is ambiguous.........

If the question is y = -(1/3)X -[-(1/2)]

Simplifying by removing square brackets gives y = -(1/3)X + (1/2)
Normally written as y = -1/3X + 1/2
Read as Y equals minus one third "X" plus one half
OR in decimal form to avoid fractions y = -0.3333X + 0.5
The minus refers to all of the one third "X" not just the minus 1
Although (-1) / (3)X is the same it is still -(1/3)X

the equation is in the form y = mx + c
m is the slope (=ve) and c is the "y" intercept (+ve)
So m = -1/3 OR -(1/3) or -0.3333 all are the same Read as minus one third.
The "y" intercept is the value of "c" which is +(1/2) or simply +1/2 or just 1/2 or +0.5 or just 0.5.
...........................................

If you mean in your question y = -(1/3)X -[(1/2)]

Simplifying by removing square brackets gives y = -(1/3)X - (1/2)
Normally written as y = -1/3X - 1/2
Read as Y equals minus one third "X" minus one half
OR in decimal form to avoid fractions y = -0.3333X - 0.5
The minus refers to all of the one third "X" not just the minus 1
Although (-1) / (3)X is the same it is still -(1/3)X

the equation is still in the form y = mx + c OR y = +mx + c
and to compare your equation is actually y = +(-m)x + (-c)
m is the slope (-ve) and c is the "y" intercept (-ve)
So m = -1/3 OR -(1/3) or -0.3333 all are the same Read as minus one third.
The "y" intercept is the value of "c" which is -(1/2) or simply -1/2 or -0.5.
...........................................

Hopefully you can figure out which matches you original equation.

Regards the -ve in front of all of a fraction is the same as -ve on the top and + on bottom
OR vice=versa +ve on top and -ve on bottom

If you divide or multiply two unlike signs the overall result is negative.

[HallsofIvy]

However, note that "y= (-1/3)x+ 1/2" is NOT the same as "y= -0.3333x+ 0.5". 0.3333 is approximately equal to 1/3 but not the same.

[Guest]

I am not same Guest as above...Ill call myself GuestWho....

Mkl....Your question and answer is ambiguous.........

If the question is y = -(1/3)X -[-(1/2)]

Simplifying by removing square brackets gives y = -(1/3)X + (1/2)
Normally written as y = -1/3X + 1/2

I disagree with that. I would say that it would be "normally written" as y= -(1/3)x+ 1/2 or y= (-1/3)x+ 1/2,
"y= -1/2x+ 1/2" is [tex]y= -\frac{1}{2x}+ \frac{1}{2}[/tex].

Read as Y equals minus one third "X" plus one half
OR in decimal form to avoid fractions y = -0.3333X + 0.5

And I disagree with this. 1/3 is NOT equal to 0.3333.

The minus refers to all of the one third "X" not just the minus 1
Although (-1) / (3)X is the same it is still -(1/3)X

the equation is in the form y = mx + c
m is the slope (=ve) and c is the "y" intercept (+ve)
So m = -1/3 OR -(1/3) or -0.3333 all are the same Read as minus one third.
The "y" intercept is the value of "c" which is +(1/2) or simply +1/2 or just 1/2 or +0.5 or just 0.5.
...........................................

If you mean in your question y = -(1/3)X -[(1/2)]

Simplifying by removing square brackets gives y = -(1/3)X - (1/2)
Normally written as y = -1/3X - 1/2
Read as Y equals minus one third "X" minus one half
OR in decimal form to avoid fractions y = -0.3333X - 0.5
The minus refers to all of the one third "X" not just the minus 1
Although (-1) / (3)X is the same it is still -(1/3)X

the equation is still in the form y = mx + c OR y = +mx + c
and to compare your equation is actually y = +(-m)x + (-c)
m is the slope (-ve) and c is the "y" intercept (-ve)
So m = -1/3 OR -(1/3) or -0.3333 all are the same Read as minus one third.
The "y" intercept is the value of "c" which is -(1/2) or simply -1/2 or -0.5.
...........................................

Hopefully you can figure out which matches you original equation.

Regards the -ve in front of all of a fraction is the same as -ve on the top and + on bottom
OR vice=versa +ve on top and -ve on bottom

If you divide or multiply two unlike signs the overall result is negative.