Question

Match the lines m and n to the statements they represent

Answer 1

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

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

`(x_1,y_1) = (13,3)` -- At point E

`(x_2,y_2) = (6,-4)` -- At point B

`(x_3,y_3) = (2,-8)` -- At point D

For n

`(x_1,y_1) = (-2,4)` -- At point A

`(x_2,y_2) = (6,-4)` -- At point B

`(x_3,y_3) = (12,-10)` -- At point C

Test for Statement A:

Set of point with a sum of 2

i.e.

`x + y = 2`

For m

`(x_1,y_1) = (13,3)` -- At point E

`x_1 + y_1 = 13 + 3 = 16`

This statement is not true for line m

For n

`(x_1,y_1) = (-2,4)` -- At point A

`x_1 + y_1 = -2 + 4 = 2`

`(x_2,y_2) = (6,-4)` -- At point B

`x_2 + y_2 = 6- 4 = 2`

`(x_3,y_3) = (12,-10)` -- At point C

`x_3 + y_3 = 12- 10 = 2`

This statement is true for line n

Test for Statement 2:

Set of points where y is x - 10

i.e.

`y = x - 10`

For m

`(x_1,y_1) = (13,3)` -- At point E

`y_1 = x_1 - 10`

`3 = 13 - 10`

`3 = 3`

`(x_2,y_2) = (6,-4)` -- At point B

`y_2 = x_2 - 10`

`-4 = 6 - 10`

`-4 = - 4`

`(x_3,y_3) = (2,-8)` -- At point D

`y_3 = x_3 - 10`

`-8 = 2 - 10`

`-8 = -8`

This statement is true for line m