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Answer:
Line n: A set of points where the coordinates of each point have a sum of 2
Line m: A set of points where the y-coordinate of each point is 10 less than the x-coordinate
Step-by-step explanation:
Given
Lines m and n (See attachment)
Required
Interpret both lines
First, we pick few coordinates of line m and then line n.
For m
[tex](x_1,y_1) = (13,3)[/tex] -- At point E
[tex](x_2,y_2) = (6,-4)[/tex] -- At point B
[tex](x_3,y_3) = (2,-8)[/tex] -- At point D
For n
[tex](x_1,y_1) = (-2,4)[/tex] -- At point A
[tex](x_2,y_2) = (6,-4)[/tex] -- At point B
[tex](x_3,y_3) = (12,-10)[/tex] -- At point C
Test for Statement A:
Set of point with a sum of 2
i.e.
[tex]x + y = 2[/tex]
For m
[tex](x_1,y_1) = (13,3)[/tex] -- At point E
[tex]x_1 + y_1 = 13 + 3 = 16[/tex]
This statement is not true for line m
For n
[tex](x_1,y_1) = (-2,4)[/tex] -- At point A
[tex]x_1 + y_1 = -2 + 4 = 2[/tex]
[tex](x_2,y_2) = (6,-4)[/tex] -- At point B
[tex]x_2 + y_2 = 6- 4 = 2[/tex]
[tex](x_3,y_3) = (12,-10)[/tex] -- At point C
[tex]x_3 + y_3 = 12- 10 = 2[/tex]
This statement is true for line n
Test for Statement 2:
Set of points where y is x - 10
i.e.
[tex]y = x - 10[/tex]
For m
[tex](x_1,y_1) = (13,3)[/tex] -- At point E
[tex]y_1 = x_1 - 10[/tex]
[tex]3 = 13 - 10[/tex]
[tex]3 = 3[/tex]
[tex](x_2,y_2) = (6,-4)[/tex] -- At point B
[tex]y_2 = x_2 - 10[/tex]
[tex]-4 = 6 - 10[/tex]
[tex]-4 = - 4[/tex]
[tex](x_3,y_3) = (2,-8)[/tex] -- At point D
[tex]y_3 = x_3 - 10[/tex]
[tex]-8 = 2 - 10[/tex]
[tex]-8 = -8[/tex]
This statement is true for line m
