From a Demand Schedule to a Graph
A demand schedule lists quantities buyers plan to purchase at specified prices, with other relevant conditions held fixed. A graph presents those same price-quantity pairs visually. The task is a translation: each row in the schedule becomes one point, and the points are then traced in the order appropriate to the graph.
The key convention is that quantity is measured along the horizontal axis and price along the vertical axis. This means that a schedule entry with quantity 24 units at a price of $6 becomes the point \((24,6)\), not \((6,24)\). The first coordinate is always the horizontal position; the second is the vertical position.
The schedule gives observations at particular prices. The graph should include every listed pair, each plotted once. A reader should be able to identify what is measured on each axis, the units, and the scale. Without that information, the location of a point is ambiguous: a horizontal distance might mean dollars, packages, or hundreds of units.
Set Up the Axes Before Plotting
First draw two perpendicular axes. Label the horizontal axis with the good and its quantity unit, such as “Quantity (boxes per week).” Label the vertical axis with price and its unit, such as “Price (dollars per box).” Begin each scale at zero unless the task explicitly calls for another origin. Starting at zero makes the displayed distances easier to interpret and avoids visually exaggerating small differences.
Next choose a scale for each axis. The scale must include every schedule value and should use the available graph area reasonably well. Equal distances on an axis must represent equal numerical changes: for example, if each grid interval represents 5 boxes, every interval on that axis represents 5 boxes. The vertical and horizontal axes do not need to use the same numerical interval because they measure different units.
A useful setup sequence is:
Identify the smallest and largest quantities and prices in the schedule. Include the largest values on the corresponding axes.
Choose intervals that are easy to count and that allow all observations to fit. For example, intervals of 2, 5, or 10 may be more readable than intervals of 3.7.
Write what each axis measures and specify the units. Add a descriptive title if the graph could otherwise be mistaken for another graph.
For every schedule row, write quantity first and price second, then plot that coordinate.
Show the schedule’s path through the points. If the instructions do not specify a smooth curve, straight line segments between adjacent plotted points provide a clear trace.
This coordinate rule follows directly from how a Cartesian graph locates a point. The first coordinate determines the horizontal position and the second determines the vertical position. Since the standard demand graph assigns quantity to the horizontal axis and price to the vertical axis, the schedule entry \((Q,P)\) must be plotted by moving to quantity \(Q\) first and price \(P\) second. Reversing the entries would instead place price horizontally and quantity vertically.
Worked Examples
Worked Example: Plotting a Schedule With Evenly Spaced Values
A hypothetical campus kiosk records the following weekly schedule for reusable water bottles. Plot the schedule using price in dollars per bottle and quantity in bottles per week.
| Price per bottle ($) | Quantity per week (bottles) |
|---|---|
| 2 | 30 |
| 4 | 24 |
| 6 | 18 |
| 8 | 12 |
Method. Find the ranges first. Prices range from $2 to $8, and quantities range from 12 to 30 bottles. Use quantity on the horizontal axis and price on the vertical axis. A convenient horizontal scale is 0, 5, 10, 15, 20, 25, 30; a convenient vertical scale is 0, 2, 4, 6, 8.
Convert each row to a point, placing quantity first:
- At price $2, quantity is 30, so plot \((30,2)\).
- At price $4, quantity is 24, so plot \((24,4)\).
- At price $6, quantity is 18, so plot \((18,6)\).
- At price $8, quantity is 12, so plot \((12,8)\).
The points fit within the stated axis ranges. Trace the schedule through \((30,2)\), \((24,4)\), \((18,6)\), and \((12,8)\), using straight segments between adjacent observations if no other tracing instruction is given.
Check. Each point’s horizontal coordinate matches the quantity column, and its vertical coordinate matches the price column. A common mistake is to plot \((2,30)\) for the first row; that reverses the standard axes and would put a price of $2 on the horizontal scale.
Worked Example: Choosing Scales for Uneven Quantities
A hypothetical print shop estimates how many custom desk calendars buyers will order at several prices. Plot the schedule. Quantities are measured in calendars per month.
| Price per calendar ($) | Quantity per month |
|---|---|
| 5 | 7 |
| 10 | 13 |
| 15 | 22 |
| 20 | 28 |
Method. The quantity values extend from 7 to 28, so an axis ending at 30 includes every point and uses the graph area effectively. Mark the horizontal axis 0, 5, 10, 15, 20, 25, 30 calendars. The vertical values range from $5 to $20; mark the price axis 0, 5, 10, 15, 20 dollars.
The plotted coordinates are \((7,5)\), \((13,10)\), \((22,15)\), and \((28,20)\). For example, \((13,10)\) is located by moving horizontally to 13 calendars, then vertically to $10. The value 13 lies between the horizontal marks for 10 and 15: it is 3 of the 5 units beyond 10, or \(3/5\) of the interval. Likewise, 22 lies \(2/5\) of the way from 20 to 25.
Plot all four points and trace through them in the schedule’s order. The nonconsecutive quantities do not require changing the interval size: the axis still uses equal intervals of 5, and points such as 13 and 22 are placed between those marks according to their numerical positions.
Check. The axis endpoints, 30 calendars and $20, include the largest values in the schedule. A common mistake is to space the four quantity values equally just because they appear in four rows. Their numerical gaps are 6, 9, and 6, so their horizontal gaps on a correctly scaled graph must reflect those different amounts.
Worked Example: Reordering a Schedule Before Plotting
A hypothetical neighborhood tool library records the following weekly schedule for borrowing garden trimmers. The schedule is listed by quantity rather than in increasing price order. Plot the points and give a clear tracing order.
| Quantity per week (trimmers) | Price per week ($) |
|---|---|
| 16 | 12 |
| 4 | 24 |
| 12 | 16 |
| 8 | 20 |
Method. The column order differs from the usual written form, so read the headings carefully. The first coordinate is still quantity and the second is still price. The four schedule points are \((16,12)\), \((4,24)\), \((12,16)\), and \((8,20)\).
For readable scales, mark the horizontal axis from 0 to 20 trimmers in intervals of 4, and the vertical axis from $0 to $24 in intervals of $4. Each point lands exactly on a grid intersection: \((16,12)\), \((4,24)\), \((12,16)\), and \((8,20)\).
To trace the schedule in its listed price order, read the prices from $12, $24, $16, to $20 and follow the matching points: \((16,12)\), \((4,24)\), \((12,16)\), \((8,20)\). The order in which rows are printed does not change the coordinates. If you prefer to trace from the lowest listed price to the highest, sort the rows by price first: \((16,12)\), \((12,16)\), \((8,20)\), \((4,24)\). State or preserve the order consistently.
Check. Both axes include the maximum entries: 16 is below 20 trimmers and $24 is at the top of the price scale. A common mistake is to treat the schedule’s first row as necessarily the lowest price or to swap columns without checking their headings. Here the first row has price $12, while the second row has the highest price, $24.
Tracing the Curve and Reading the Graph
Once the points are plotted, trace through them so the graph visibly represents the schedule. A curve drawn through the observations is a visual summary of the listed price-quantity pairs. When a task asks only for a graph from a finite schedule, do not claim that the schedule supplies exact quantities at prices that were not listed. Connecting observations makes the pattern easier to see; it does not add new measured rows to the original schedule.
If the problem explicitly requests a smooth curve, draw a smooth trace through the plotted points. Otherwise, connecting adjacent observations with straight segments is a practical plotting convention. In either case, take care that the trace passes through every listed point and does not obscure the axes or their labels. Do not extend the curve past the observed range unless instructed to do so.
A graph can also be checked by reading a point back into the schedule. For a plotted point \((Q,P)\), move across from its horizontal coordinate and up or down to its vertical coordinate. The result should say: “At price \(P\), the schedule lists quantity \(Q\).” For instance, the point \((12,20)\) means 12 trimmers per week at a weekly price of $20, not 20 trimmers at $12.
Common Plotting Errors
- Reversing the coordinates. The schedule may show price first, but the graph’s point is still quantity first: \((Q,P)\).
- Reversing the axes. The horizontal axis is quantity and the vertical axis is price. Label both axes before plotting.
- Using unequal intervals accidentally. Equal visual distances on one axis must represent equal numerical changes. Mark each interval consistently.
- Choosing an axis that excludes a value. Check the largest quantity and price before choosing endpoints.
- Spacing observations equally regardless of their values. Plot each quantity and price according to the numerical scale, not according to row number.
- Assuming a connecting line is extra schedule data. The schedule specifies its listed pairs; a trace helps display them but does not by itself state exact values between them.
The graphing skill here is deliberately limited to representing the schedule accurately. Interpreting why the points have a particular arrangement is a separate economic question. First make sure the axes, coordinates, and plotted locations faithfully reproduce the information supplied.
Check Your Understanding
For each problem, identify the coordinate pairs and make the specified plotting decisions before checking the answer.
- A hypothetical meal service has a schedule of price per lunch ($): 6, 9, 12, and quantities per week: 40, 32, 24. State all plotted points and identify which variable belongs on each axis. (Answer: \((40,6)\), \((32,9)\), \((24,12)\); quantity is horizontal and price is vertical.)
- A schedule lists price per seed packet as $4, $8, and $12, with quantities 9, 17, and 26 packets. Give axis endpoints that include all observations using convenient intervals of 5 units on both axes, and state the points. (Answer: quantity axis 0–30 packets, price axis 0–15 dollars; points \((9,4)\), \((17,8)\), \((26,12)\).)
- A schedule is headed “Quantity (rental days)” then “Price ($)” and lists (6, 18), (12, 12), and (18, 6). What are the plotted coordinates? Explain the coordinate order. (Answer: \((6,18)\), \((12,12)\), and \((18,6)\); the headings already give quantity first and price second, matching horizontal then vertical.)
- A graph uses horizontal marks 0, 10, 20, 30 and vertical marks $0, $5, $10, $15. A schedule entry is quantity 25 units at price $12.50. Locate the point relative to the scale marks. (Answer: \((25,12.50)\), halfway between 20 and 30 horizontally and halfway between $10 and $15 vertically.)
- A schedule lists, in this order, quantity 14 at price $7, quantity 6 at price $21, and quantity 10 at price $14. Give the points and the order for tracing from lowest to highest listed price. (Answer: Points are \((14,7)\), \((6,21)\), and \((10,14)\); lowest-to-highest price order is \((14,7)\), \((10,14)\), \((6,21)\).)