* Easy Linear Question. Slope and y intercept. Thanks!

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Homework Statement



Determine the slope and y-intercept of the line: 1/2y = x - 1 - Graph the line


Homework Equations



I know this is a simple one, but im having troubles with it. Can someone lay out how they got the slope, and then how they got the y-intercept. pointing out the steps ?



The Attempt at a Solution



I can't figure out how to get the slope. I must be just missing a major step lol.

Thanks!!
 

Answers and Replies

  • #2
rock.freak667
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The Attempt at a Solution



I can't figure out how to get the slope. I must be just missing a major step lol.

Thanks!!

You need to put the form in the equation y=mx+c, 'm' is the gradient and 'c' is the y-intercept.

So try multiplying by some number to get it into that form.
 
  • #3
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You need to put the form in the equation y=mx+c, 'm' is the gradient and 'c' is the y-intercept.

So try multiplying by some number to get it into that form.

First off, what do I do about the 1/2y ?
 
  • #4
eumyang
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You need to put the form in the equation y=mx+c, 'm' is the gradient and 'c' is the y-intercept.

So try multiplying by some number to get it into that form.

First off, what do I do about the 1/2y ?

Wait a minute. What is the original equation? Is it this:
[tex]\frac{1}{2y} = x - 1[/tex]
or this?
[tex]\frac{1}{2}y = x - 1[/tex]

It looks like rock.freak667 is assuming the later. (By the way, you have to be careful when typing in equations. Either learn LaTex or use parentheses.) You want to isolate the y. As he/she said, you multiply both sides of the equation by some number to get the y by itself on the left side. So, what do you do?


69
 
  • #5
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[tex]\frac{1}{2}y = x - 1[/tex]



Wait a minute. What is the original equation? Is it this:
[tex]\frac{1}{2y} = x - 1[/tex]
or this?
[tex]\frac{1}{2}y = x - 1[/tex]

It looks like rock.freak667 is assuming the later. (By the way, you have to be careful when typing in equations. Either learn LaTex or use parentheses.) You want to isolate the y. As he/she said, you multiply both sides of the equation by some number to get the y by itself on the left side. So, what do you do?


69
 
  • #6
HallsofIvy
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RockFreak667 assume the OP meant [itex](1/2)y= x- 1[/itex] because [itex]\frac{1}{2y}= x- 1[/itex] is not a line and doesn't have a "slope"!

To solve for y, multiply both sides by 2. Once you have it in the form y= mx+ b, m is the slope and b is the y-intercept.
 
  • #7
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RockFreak667 assume the OP meant [itex](1/2)y= x- 1[/itex] because [itex]\frac{1}{2y}= x- 1[/itex] is not a line and doesn't have a "slope"!

To solve for y, multiply both sides by 2. Once you have it in the form y= mx+ b, m is the slope and b is the y-intercept.

why do I divide both sides by 2? where did u get 2 from?
 
  • #8
rock.freak667
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why do I divide both sides by 2? where did u get 2 from?


if you have 0.5y=x-1, how would you get 'y' only on the left side? Multiply by 2 right?
 
  • #9
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if you have 0.5y=x-1, how would you get 'y' only on the left side? Multiply by 2 right?

Just so I get the steps right.

Why pick 2?

And you say multiply both sides by 2. So, can u break that down? How does that become:
y = 2(x -1)

Appreciate it!
 
  • #10
rock.freak667
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Just so I get the steps right.

Why pick 2?

And you say multiply both sides by 2. So, can u break that down? How does that become:
y = 2(x -1)

Appreciate it!

(1/2)y= (x-1)

multiply by 2
2*(1/2)y=2*(x-1)

y=2(x-1)
 
  • #11
eumyang
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RockFreak667 assume the OP meant [itex](1/2)y= x- 1[/itex] because [itex]\frac{1}{2y}= x- 1[/itex] is not a line and doesn't have a "slope"!
Oh, I know. I was being difficult on purpose.

Why pick 2?

And you say multiply both sides by 2. So, can u break that down? How does that become:
y = 2(x -1)
You pick 2 because 2 is the reciprocal of 1/2. When you multiply (1/2)y by 2, the 1/2 and 2 "cancel each other out," leaving with the y by itself. If I have another linear equation like
[tex]\frac{1}{6}x = 4[/tex]
the reciprocal of 1/6 is 6, so I multiply both sides by 6 to isolate the x:
[tex]\begin{aligned}
6 \cdot \frac{1}{6}x &= 6 \cdot 4 \\
x &= 24
\end{aligned}[/tex]

One more thing:
y = 2(x -1)
This is not yet in slope-intercept form, y = mx + b. You still have one more thing to do.


69
 
Last edited:
  • #12
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Oh, I know. I was being difficult on purpose.


You pick 2 because 2 is the reciprocal of 1/2. When you multiply (1/2)y by 2, the 1/2 and 2 "cancel each other out," leaving with the y by itself. If I have another linear equation like
[tex]\frac{1}{6}x = 4[/tex]
the reciprocal of 1/6 is 6, so I multiply both sides by 6 to isolate the x:
[tex]\begin{aligned}
6 \cdot \frac{1}{6}x &= 6 \cdot 4 \\
x &= 24
\end{aligned}[/tex]

One more thing:

This is not yet in slope-intercept form, y = mx + b. You still have one more thing to do.


69

What is left to do? Just take out the bracket, so it becomes:

y = 2x -1
 
  • #13
eumyang
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What is left to do? Just take out the bracket, so it becomes:

y = 2x -1
No, you can't just "take out the bracket." You have to apply the distributive property:
a(b + c) = ab + ac


69
 
  • #14
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No, you can't just "take out the bracket." You have to apply the distributive property:
a(b + c) = ab + ac


69

[tex]\stackrel{1}/{2}[/tex]
 
  • #15
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If you mean y = 2x - 1/2, no.
You had y = 2(x - 1). If you expand the right side as eumyang suggested, what do you get?
 

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