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 June 15th, 2010, 09:44 AM #1 Newbie   Joined: Jun 2010 Posts: 24 Thanks: 0 quick q given 2x+3y=12, what is the slope, y intercept, and what would the graph look like is the slope??? m= -3 y int: b= 6 any help? thanks
 June 15th, 2010, 10:15 AM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: quick q The slope and y intercept are most easily identified when the equation is in "slope intercept form" y=mx + b
June 15th, 2010, 10:25 AM   #3
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Re: quick q

Quote:
 Originally Posted by bignick79 given 2x+3y=12, what is the slope, y intercept, and what would the graph look like is the slope??? m= -3 y int: b= 6 any help? thanks
Remeber, if you can get a linear equation like this one into the following form:

$y= mx + b$

Then you know the y-intercept and the slope.

$SLOPE= m$
$Y-INTERCEPT= b$

So, we have the equation:

$2x+3y=12$

Subtracting 2x from both sides gives:

$3y= 12 - 2x$

Then dividing both sides (meaning the whole of both sides) by 3 gives:

$y= \frac{12 - 2x}{3}$

this becomes, by basic rules of fractions, the following:

$y= \frac{-2}{3}x + 4$

This is in the form:

$y= mx + b$

So,

$m= \frac{-2}{3}$

and

$b= 4$

This graph would look like a line, slanted from top left to bottom right, intersecting the y-axis at four. Basically draw a point at (0, 4) and move down two [-2 in the slope, m] and to the right 3 [+3 in the slope, m] to find your next point. Continue this to get a picture of the graph, in both directions. Hope this helps, anymore questions post them here and I'll try to clarify.

June 15th, 2010, 10:41 AM   #4
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Re: quick q

Hello, bignick79!

Quote:
 Given:[color=beige] .[/color]$2x\,+\,3y \:=\:12$ What is the slope, y-intercept, and what would the graph look like?

Get the equation into the form:[color=beige] .[/color]$y \:=\:mx\,+\,b$
[color=beige]. . [/color]That is, solve for $y.$

$\text{We have: }\:2x\,+\,3y \:=\:12$

[color=beige]. . . [/color]$\text{Then: }\;\;\;\;\;\;\;\;\;3y \:=\:-2x\,+\,12$

[color=beige]. .[/color]$\text{Finally: }\;\;\;\;\;\;\;\;\;y \:=\;-\frac{2}{3}x \,+\,4$
[color=beige]. . . . . . . . . . . . . . . . . . [/color]$\uparrow$[color=beige] - - [/color]$\uparrow$
[color=beige]. . . . . . . . . . . . . . . . [/color]slope[color=beige] . [/color]y-intercept

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

This line has a y-intercept at $(0,\,4)$

$\text{The slope is: }\:\frac{-2}{+3} \:=\:\frac{\text{rise}}{\text{run}}$

$\text{It has a "run" of +3 . . . and a "rise" of -2.}$

$\text{So, from (0, 4), we move: right 3 units and down 2 units.}$
[color=beige]. . [/color]$\text{This locates a second point and we can draw the line.}$

Code:
        |
*       |
*   |4        +3
o - - - - - - - - - +
|   *               :
|       *           : -2
|           *       :
|               *   :
|                   o
- - - + - - - - - - - - - - - * - - -
|                           *
|

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