Final answer:
Option 3: (1,0); (0,0) is the correct answer to make both statements false, indicating the incorrect characteristics of nonproportional and proportional relationships, as nonproportional relationships do not have to pass through the origin and proportional relationships do intercept the y-axis at (0,0).
Step-by-step explanation:
When completing each statement to result in the truth value F (False) for the given sentences about proportional and nonproportional relationships, we need to select options that incorrectly describe the characteristics of these types of relationships in a coordinate plane graph.
Nonproportional relationships do not necessarily pass through the origin ((0, 0)). However, a proportional relationship implies that the graph will have a constant ratio between the two variables, and any such line will always pass through the origin. Therefore, to make the statements false, we need to select options that misrepresent these facts.
- If (1, 0) then the graph of a nonproportional relationship passes through the origin (False).
- If (1, 0) the graph of a proportional relationship intercepts the y-axis at (0, 0) (False).
The option that makes both statements false is Option 3: (1,0); (0,0). This option suggests that a graph with a y-intercept of (1, 0) would represent a nonproportional relationship that passes through the origin, which is incorrect, and also implies that a graph of a proportional relationship does not intercept the y-axis at (0, 0), but we know that it does.