Baldwin Union Free Schools District 7th grade Mathematics Scope ... - Free Printable

I will solve this problem by analyzing each of the 8 graphs to determine if they represent a proportional or non-proportional relationship. The key criterion, as stated in the image, is whether the graph passes through the origin (0,0).

I'll examine each graph one by one.

Graph 1:
- This is a straight line with a negative slope.
- Looking at the graph, it appears to pass through the origin (0,0), where the x-axis and y-axis intersect.
- Since it passes through the origin, this is a proportional relationship.

Graph 2:
- This is a straight line with a positive slope.
- The line clearly does not pass through the origin; it intersects the y-axis at a positive value (approximately y=2) and the x-axis at a negative value.
- Since it does not pass through the origin, this is a non-proportional relationship.

Graph 3:
- This is a straight line with a negative slope.
- The line intersects the y-axis at a positive value (approximately y=4) and the x-axis at a positive value (approximately x=2).
- It does not pass through the origin, so this is a non-proportional relationship.

Graph 4:
- This is a straight line with a positive slope.
- The line passes directly through the origin (0,0).
- Since it passes through the origin, this is a proportional relationship.

Graph 5:
- This is a straight line with a very small positive slope.
- The line passes directly through the origin (0,0).
- Since it passes through the origin, this is a proportional relationship.

Graph 6:
- This is a straight line with a positive slope.
- The line intersects the y-axis at a negative value (approximately y=-2) and the x-axis at a positive value (approximately x=4).
- It does not pass through the origin, so this is a non-proportional relationship.

Graph 7:
- This is a straight line with a negative slope.
- The line intersects the y-axis at a positive value (approximately y=3) and the x-axis at a positive value (approximately x=6).
- It does not pass through the origin, so this is a non-proportional relationship.

Graph 8:
- This is a straight line with a very steep positive slope.
- The line passes directly through the origin (0,0).
- Since it passes through the origin, this is a proportional relationship.

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Final Answer:

Based on the analysis of each graph using the criterion that a proportional relationship must pass through the origin (0,0):

- Graph 1: Proportional
- Graph 2: Non-proportional
- Graph 3: Non-proportional
- Graph 4: Proportional
- Graph 5: Proportional
- Graph 6: Non-proportional
- Graph 7: Non-proportional
- Graph 8: Proportional