Answer:
see the attached for the table and rules
Step-by-step explanation:
a) A graph of the given points shows they lie on the same line, one with a slope of 3 and a y-intercept of 2. Thus the rule is ...
y = 3x +2
see the attachment for table values
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b) The ratios of given points are all the same: y/x = 5/2, so that is the constant of proportionality:
y = (5/2)x
see the attachment for table values
So for the rhombus to carry onto itself, it needs to start in one position and end up in that same position. In this case, (x,y) will need to end up on (x,y) after the reflections are done. Here what the options do:
A: y-axis, x-axis, y-axis
(x,y) -> (-x,y) -> (-x,-y) -> (x,-y)
B: x-axis, y-axis, y-axis
(x,y) -> (x,-y) -> (-x,-y) -> (x,-y)
C: y=x, x-axis, y=x, y-axis
(x,y) -> (y,x) -> (y,-x) -> (-x,y) -> (x,y)
D: x-axis, y=x, x-axis, y=x
(x,y) -> (x,-y) -> (-y,x) -> (-y,-x) -> (-x,-y)
The only option that starts as (x,y) and ends as (x,y) is C: y=x, x-axis, y=x, y-axis, therefore making that the correct answer.
