Graphing Tables Worksheet: Turn Input-Output Tables into Coordinate Graphs

Algebra and Function Practice

An input-output table lists pairs of values: each input is paired with exactly one output. To graph the relationship, treat each input as the x-coordinate and its output as the y-coordinate, forming ordered pairs (input, output). Plot each pair on a coordinate grid, then connect the points when the pattern is consistent. This lesson focuses only on table-to-graph conversion: reading tables, plotting points, connecting them, and identifying the pattern. It does not cover writing equations from tables or graphing directly from slope-intercept form.

Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.

Reading an Input-Output Table

An input-output table usually has two columns. The input column gives x-values; the output column gives the corresponding y-values. Each row is one ordered pair. For example, if input 2 gives output 5, the ordered pair is (2, 5).

Check that each input appears once. If an input repeats with different outputs, the table does not represent a function, and connecting points may not produce a single line. For this lesson, assume each input has one output.

1. Read the column headings and confirm which column is input and which is output.
2. Copy each row as an ordered pair in the form (input, output).
3. Check arithmetic: for each row, verify the output matches the stated pattern if one is given.
4. List the ordered pairs in order from smallest input to largest input.

Plotting Ordered Pairs on a Coordinate Grid

A coordinate grid has a horizontal x-axis and a vertical y-axis. The origin is (0, 0). To plot (3, 4), start at the origin, move 3 units right along the x-axis, then 4 units up parallel to the y-axis. Mark the point and label it if needed.

Use consistent scale. If each grid square represents 1 unit, say so. If the table has large values, choose a scale that fits the grid, such as 2 units per square, and label the axes clearly. Measure the actual grid you use rather than assuming a standard size.

1. Draw and label the x-axis and y-axis; mark the origin.
2. Choose a scale that fits all input and output values on the grid.
3. For each ordered pair, move along x first, then along y.
4. Mark each point clearly; use a small dot or cross.
5. Check each point by reading its coordinates back from the grid.

Connecting Points and Identifying the Pattern

If the points lie on a straight line, place a ruler through them and draw one straight line. If the points do not lie on a straight line, connect them in input order with segments only if the context implies a sequence; otherwise leave them as separate points and describe the pattern.

Describe the pattern in words: as input increases by 1, does output increase by a constant amount, decrease, or change unevenly? For a straight line, the constant change in output per 1-unit increase in input is the pattern. For example, outputs 3, 5, 7, 9 increase by 2 each time.

1. Lay a ruler along the plotted points to test whether they are collinear.
2. If collinear, draw one straight line through all points and extend it slightly beyond the first and last points.
3. If not collinear, do not force a straight line; describe how the output changes as input increases.
4. State the pattern using simple arithmetic, such as add 2 to the output for each increase of 1 in the input.

Checking a Completed Graph

A correct graph has one plotted point per table row, each point at the correct coordinates, and a line or point set that matches the pattern. Check at least two points by reading coordinates from the grid and comparing them to the table.

Watch for reversed coordinates: plotting (output, input) instead of (input, output) is a common error. Also check axis labels and scale. If the line passes through the origin, the table should include (0, 0) or the pattern should produce it.

1. Count the plotted points and compare with the number of table rows.
2. Read two points from the grid and match them to table rows.
3. Confirm the line or point pattern matches the described output change.
4. Check axis labels, scale, and origin placement.

Worked example

A table shows input 0, 1, 2, 3 with outputs 1, 3, 5, 7. Plot the ordered pairs on a grid with 1 unit per square, connect them, and describe the pattern.

Four practice exercises

Common mistakes

• Plotting output first and input second, producing (y, x) instead of (x, y). Always write the ordered pair as (input, output) before plotting; say the pair aloud as 'input comma output'.
• Connecting points with a straight line when the table does not show a constant change. Test collinearity with a ruler first; if points are not collinear, leave them separate and describe the uneven pattern.
• Using an unlabeled or inconsistent scale on the axes. Label each axis and state the scale, such as 1 unit per square, before plotting any points.
• Skipping a table row or duplicating a point. Number the table rows and tick each one after plotting its point; count points at the end.

Self-check rubric

• All ordered pairs are written as (input, output) and match the table rows.
• Each point is plotted at the correct coordinates on a labeled grid with a stated scale.
• Points are connected with one straight line only when collinear; otherwise left separate with a described pattern.
• The pattern is stated in simple arithmetic, such as 'output increases by 2 for each increase of 1 in input'.
• Axis labels, origin, and scale are correct and readable.
• Valid alternative: a neatly drawn point set with a described pattern earns credit even if the line is not extended beyond the plotted points, provided the description is correct.

Questions and answers