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y=2x+1 choosing a value for x and then y

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2 Answers

Hi Amber;
y=2x+1 
The equation is in slope-intercept form...
y=mx+b
m is the slope, 2.
b is the y-intercept, the value of y when x=0.  b=1, corresponding to the point, (0,1).
The x-intercept is the value of x when y=0.
0=2x+1
-1=2x
-1/2=x
(-1/2,0)
Plot these two points, and draw a line.  The slope of the equation is 2.
As your line moves up 2 units, it will also move to the right 1 unit.
As your line moves down 2 units, it will also move to the left 1 unit.

3x+2y=12
This equation is in standard format...
Ax+By=C, A>0
Let's calculate the x-intercept by setting y=0...
3x+[(2)(0)]=12
3x=12
x=4
(4,0)
Let's calculate the y-intercept by setting x=0...
[(3)(0)]+2y=12
2y=12
y=6
(0,6)
The slope of the line of an equation in standard format is calculated by...
-A/B...
-3/2
As your line moves up 3 units, it moves to the left 2 units.
As your line moves down 3 units, it moves to the right 2 units.
 
Hi Amber!  It looks like you have two separate equations to work with... 
...unless you are looking for the point at which they cross, and they will intersect as long as they are not parallel...  we'll get to that later, if needed, no problem!
 
Starting with the first equation:
y=2x+1
I always use four numbers to graph; three will work, but I like to be sure.
         X  ,  Y 
       -1   ,      
        0   ,
        1   ,
        5   ,
-1,0 & 1 are going to be the three easiest to work with.  5 is just another number I picked to double check.
Starting with -1, plug it in and find out what Y will equal:
y=  2x+1         original equation
y=  2(-1)+1     substitute -1 for x
y= -2+1          multiply 2(-1) = -2
y= -1              add -2+1= -1 
Write in -1 under Y next to the X you used (THEY WILL NOT ALWAYS BE THE SAME; THEY RARELY ARE!)
 
         X  ,    Y 
       -1   ,  -1    
        0   ,
        1   ,
        5   ,
 
Now, start over using the next number for x and substitute in:
y=2x+1
y=2(0)+1
y=0+1
y=1
 
         X  ,  Y 
       -1   ,  -1   
        0   ,    0
        1   ,
        5   ,
 
Keep going!  Two more to do.  Remember, although you could probably do some in your head, it is EXTREMELY important to write down all steps.  It will make things EXTREMELY easy in the future!
 
y=2(1)+1       y=2(5)+1
y=2+1           y=10+1
y=3               y=11
 
         X  ,  Y 
       -1   ,  -1    
        0   ,   1
        1   ,   3
        5   ,   11
 
You can check these pairs by subbing any of them into the original equation.  They should equal, of course!
Take the last pair (5,11)  
  y = 2x+1      original
11 = 2(5)+1   sub in for x and y
11 = 10+1      multiply
11=11            add
Since eleven does equal eleven, we have just proven this pair does lie on the line for the equation. 
 
Graphing will be done on graph paper:
USE GRAPH PAPER! - or at least draw lines using a ruler...
First plot each point from the ordered pair list you've created. 
Mark and label each point.
Then connect the dots.
This forms the line for the equation y=2x+1 and represents every possible solution to the equation.
 
Hope this helps! 
 
Ok, the next equation, I am going to skip the explanation and show the work... same steps.
 
 3x+2y=12
  X  ,  Y 
-1  ,
 0  ,
 1  ,
 5  ,
 
3(-1)+2y=12
-3+2y=12
-3+2y+3=12+3
2y=15
y=15/2 or 7.5
 
3(0)+2y=12
2y=12
y=6
 
and so on...
 
Hope this helps!