Michelle E. Chung

When a=1:

• The graph is a straight line because x+y=1 is same as y= -x+1.
• The graph of x+y=1 is a straight line that its slope is -1 and its y-intercept is 1.

When a=3:

• The graph is NOT a straight line.
• It looks like a top of a hat, and the coordinates of the top of the hat is (0.793701, 0.793701).
  Also, it is symmetric to y=x.

When a=5:

• The graph is NOT a straight line, either.
• It looks like a top of a hat, too, but the coordinates of the top of the hat is (0.870551, 0.870551).
  It is symmetric to y=x, too.

When a=7:

• The graph is NOT a straight line, either.
• It looks like a top of a hat, too, but the coordinates of the top of the hat is (0.905724, 0.905724).
  It is symmetric to y=x, too.

When a=9:

• The graph is NOT a straight line, either.
• It looks like a top of a hat, too, but the coordinates of the top of the hat is (0.925875, 0.925875).
  It is symmetric to y=x, too.

• As you see, the graph of when a is odd is a straight line with a curve part, which looks like a top of a hat, except when a=1(it is a straight line).
• It is symmetric to y=x.
• The curve part is getting pointier when the value of a is greater, and we actually can notice that the coordinates of the top of it is getting greater.

When a=2:

• The graph is a circle that its center is (0,0) and its radius is 1 because it is a equation of a circle.
• It is also symmetric to y=x because (0.707107, 0.707107) is on the circle.

When a=4:

• The graph is NOT a circle anymore.
• It looks like a square with some curve corners, or it looks like a flatted circle that has (0,0) as its center and radius 1, too, but one of the coordinates of the corner is (0.840896, 0.840896).
• It is also symmetric to y=x, too.

When a=6:

• The graph is NOT a circle anymore, either.
• It looks like a square with some curve corners, or it looks like a flatted circle that has (0,0) as its center and radius 1, too, but one of the coordinates of the corner is (0.890899, 0.890899).
• It is also symmetric to y=x, too.

When a=8:

• The graph is NOT a circle anymore, either.
• It looks like a square with some curve corners, or it looks like a flatted circle that has (0,0) as its center and radius 1, but one of the coordinates of the corner is (0.917004, 0.917004).
• It is also symmetric to y=x, too.

When a=10:

• The graph is NOT a circle anymore, either.
• It looks like a square with some curve corners, or it looks like a flatted circle that has (0,0) as its center and radius 1, too, but one of the coordinates of the corner is (0.933033, 0.933033).
• It is also symmetric to y=x, too.

• As you see, the graph of when a is even is a flatted circle that has (0,0) as its center and radius 1, except when a=2(it is a circle).
• It is symmetric to y=x.
• The corners of the flatted circle are getting pointier when the value of a is greater, and we actually can notice that the coordinates of the top of it are getting greater.

• As you see, it IS a flatted circle with (0,0) as its center and radius 1.
• Its corners are pointer than others, and one of the coordinates is (0.971532, 0.971532).
• It is also symmetric to y=x.

• As you see, it IS a straight line with a curve part, which looks like a top of a hat.
• The top of the hat is pointer than others, and the coordinates of it are (0.972655, 0.972655).
• It is also symmetric to y=x.