Answer:
The three points lie on a straight line
A line through the points passes through the origin
The graph shows a proportional relationship
Step-by-step explanation:
Given statements:
a) The three points do not lie on a straight line.
b) The three points lie on a straight line.
c) A line through the points passes through the origin.
d) A line through the points does not pass through the origin.
e) The graph shows a proportional relationship.
f) The graph does not show a proportional relationship.
For the first and second statements, we can see that the points are able to be connected with a straight, diagonal line (see attached graph). This makes statement a false, and statement b true.
a = false
b = true
For the third and fourth statements, we can see that on the attached (revised) graph on my answer, that the line can continue and pass through the origin, or (0,0). This means that statement c is true, and statement d is false.
c = true
d = false
For the fifth and sixth statements, we know that a relationship is proportional if it is a straight line and passes through the origin when graphed. We have already concluded above that both of these are true, so this means that the graph does represent a proportional relationship. This means that statement e is true, and statement f is false.
e = true
f = false
From the above work, we can conclude that the following statements are true:
b (The three points lie on a straight line)
c (A line through the points passes through the origin)
e (The graph shows a proportional relationship)
Hope this helps :)
