Origin Check

This worksheet helps students decide whether a graphed linear relationship is Proportional or Non-Proportional by checking whether the line passes through the origin, (0,0). Each graph shows a straight-line pattern, but some begin at zero while others start above or below it. That difference is the key. A proportional relationship must pass through the origin because when x = 0, y must also equal 0. This activity strengthens graph reading, coordinate-plane understanding, proportional reasoning, and the connection between visual patterns and equations.

For a parent, the easiest rule is: if the line goes through (0,0), it can be proportional; if it misses the origin, it is not proportional. The origin is where the x-axis and y-axis cross. It is the graphing version of saying there is no starting amount.

Learning Goals

• Recognize the Origin: Students identify the point (0,0) on a graph.
• Classify Graphs: Learners decide whether each line represents a proportional or non-proportional relationship.
• Connect Graphs to y = kx: Students understand that proportional graphs come from equations with no added starting value.
• Build Visual Reasoning: Learners use the graph itself as evidence.
• Prepare for Slope and Linear Functions: Students begin distinguishing lines through the origin from other linear relationships.

Parent-Friendly Teaching Tips

Use this routine:

1. Find the point where the axes cross.
2. Ask whether the line goes through that point.
3. If yes, classify it as Proportional.
4. If no, classify it as Non-Proportional.

For example, a line that includes:

(0,0), (1,2), (2,4), (3,6)

is proportional.

But a line that includes:

(0,2), (1,4), (2,6), (3,8)

is not proportional because it starts at 2 instead of 0.

Why This Worksheet Helps

• Makes Proportionality Visual: Students can see the difference instead of only calculating ratios.
• Connects Tables, Equations, and Graphs: The origin corresponds to the “no extra starting value” idea.
• Builds Coordinate-Plane Fluency: Learners practice reading x- and y-values.
• Prepares for Slope-Intercept Form: Students begin noticing the role of a y-intercept.
• Encourages Multiple Representations: Students see that proportionality can be identified in more than one way.

The main value of this worksheet is that it teaches students to recognize proportionality from a graphical clue. The origin, straight lines, coordinates, and proportional relationships all work together. For parents, the best reminder is: “A proportional line has to pass through zero.”