SOLUTION: 1. How do you plot x = 2y, y = x + 2, y = 2x and y = x ÷ 2 on a graph. Which one of the above formulas describes a line.

Algebra ->  Systems-of-equations -> SOLUTION: 1. How do you plot x = 2y, y = x + 2, y = 2x and y = x ÷ 2 on a graph. Which one of the above formulas describes a line.       Log On


   

Question 720757: 1. How do you plot x = 2y, y = x + 2, y = 2x and y = x ÷ 2 on a graph.
Which one of the above formulas describes a line.
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
They all describe straight lines
To see this, put them all into the
slope-intercept form
(1) +x+=+2y+
(1) +y+=+%281%2F2%29%2Ax+
-----------------
(2) +y+=+x+%2B+2+ ( don't have to change )
-----------------
(3) +y+=+2x+ ( don't have to change )
-----------------
(4) +y+=+%281%2F2%29%2Ax+ ( same as (1) )
-----------------
These all have the form +y+=+m%2Ax+%2B+b+,
where m = slope and b = y-intercept
For (1) and (3), +b+=+0+
------------------
Since 2 are the same, there is only 3 lines:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+%281%2F2%29%2Ax%2C+x%2B+2%2C++2x+%29+

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x+=+2y, y+=+x+%2B+2, y+=+2x and y+=+x%2F+2.....these are all equations of a line because you have x%5E1 and y%5E1
to plot them on a graph, all you need is to find two points for each and draw a line through
easiest way is to find x and y-intercept
1.
x+=+2y....to find x-intercept plug in y=0
x+=+2%2A0
x+=+0....... x-intercept is at (0,0)
since y-intercept will be also at 0,0), we will find a point for x=1
1=+2y
1%2F2+=y....... the point is at (1,1%2F2)
now plot points (0,0) and (1,1%2F2) on a Cartesian coordinate system and draw a line through
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2F2%29+
2.


y+=+x+%2B+2....to find x-intercept plug in y=0
0+=+x+%2B+2
x=+-2....... x-intercept is at (-2,0)

y+=+x+%2B+2....to find y-intercept plug in x=0
y+=+0+%2B+2
y=+2....... x-intercept is at (0,2)

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B2%29+
3.
y+=+2x....to find x-intercept plug in y=0
0=+2x
x+=+0....... x-intercept is at (0,0)
since y-intercept will be also at 0,0), we will find a point for x=1
y=+2%2A1
y+=2....... the point is at (1,2)
now plot points (0,0) and (1,2) on a Cartesian coordinate system and draw a line through
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%29+
4.
y+=+x%2F+2...this is same as 1. x+=+2y when you solve it for y