From a Supply Schedule to a Graph
A supply schedule organizes pairs of prices and quantities supplied. A graph makes those pairs easier to see and interpret, provided each variable is placed on the correct axis and the scale is read carefully. The central convention is that quantity is measured on the horizontal axis and price on the vertical axis. This is the reverse of how the two entries may appear in a table, so it is worth checking the axes before plotting.
In this tutorial, a quantity supplied is the amount sellers are willing and able to offer at a stated price, with the other relevant conditions held as specified. The schedule records the price and quantity supplied together for each entry. A graph must preserve those pairings: a point is not just a quantity or a price, but the two values that belong together.
For example, if a schedule says that a seller supplies 6 crates when the price is $10 per crate, the corresponding graph point is \((6,10)\). Read it as “quantity 6 at price $10,” not as a price of 6 and a quantity of 10. The horizontal coordinate answers “how many?” and the vertical coordinate answers “at what price?”
Choosing Axes, Scales, and Points
A graph is useful only if its axes and scale are clear. Label the horizontal axis “Quantity supplied” and state its unit, such as crates per week. Label the vertical axis “Price” and state its unit, such as dollars per crate. Then choose intervals that include every quantity and price in the schedule. Equal distances on an axis must represent equal changes in the measured value.
The scale does not have to begin at zero in every possible graph, but a beginner’s supply-schedule graph is usually easiest to read when each axis begins at zero. If the scale does not start at zero, make that choice explicit and be especially careful not to interpret the visual distance from the origin as if the axis started there. The numerical tick labels, not the apparent position alone, determine the value of a point.
Plot each entry by moving first to its quantity on the horizontal axis and then up or down to its price on the vertical axis. For a schedule with entries \((Q_1,P_1)\), \((Q_2,P_2)\), and so on, the plotted points are precisely those pairs. After plotting, check that every point is at the intersection of the intended quantity and price values.
Put quantity supplied, with its unit, on the horizontal axis; put price, with its unit, on the vertical axis.
Choose equal intervals that cover the smallest and largest quantities and prices in the schedule.
For an entry of quantity \(Q\) at price \(P\), locate \(Q\) horizontally and \(P\) vertically, then mark their intersection.
Check the axis labels, units, scale, and each plotted point against the original schedule.
Worked Example: Plotting a Schedule with Whole-Unit Axes
A hypothetical orchard’s weekly supply schedule is:
| Price per crate | Crates supplied per week |
|---|---|
| $4 | 0 |
| $8 | 3 |
| $12 | 7 |
| $16 | 12 |
Plot the schedule using a horizontal axis from 0 to 12 crates, marked every 2 crates, and a vertical axis from $0 to $16, marked every $2. Then state the quantity supplied at a price of $12.
Method. Convert each table row into the ordered pair \((Q,P)\), placing quantity first because it is the horizontal coordinate:
The horizontal scale covers quantities from 0 through 12, and the vertical scale covers prices from $0 through $16. Plot \((0,4)\) at quantity 0 and price $4; plot \((3,8)\) at quantity 3 and price $8; plot \((7,12)\) at quantity 7 and price $12; and plot \((12,16)\) at quantity 12 and price $16. The values 3 and 7 fall between the horizontal ticks, so their positions must be located using the stated scale rather than rounded to a nearby tick.
At price $12, read across from $12 on the vertical axis to the point \((7,12)\), then down to the horizontal axis. The quantity is 7 crates per week.
Check. The table’s $12 row gives 7 crates, and the graph point at vertical value 12 has horizontal value 7. The graph agrees with the schedule. The method avoids the common axis reversal: treating \((12,7)\) as the point would incorrectly show price $7 at quantity 12.
Reading a Price or Quantity from the Graph
To read a quantity at a stated price, start at that price on the vertical axis, move horizontally to the plotted schedule, and then move vertically to the horizontal axis. To read a price at a stated quantity, start at the quantity on the horizontal axis, move vertically to the schedule, and then horizontally to the vertical axis. These paths keep the coordinate directions straight.
When the requested value is exactly one of the schedule entries, the graph should return the same value as the table. When it lies between entries, the answer depends on what the graph represents. If the schedule consists only of listed observations, it does not specify every intermediate pair. If the task explicitly represents the points as connected by straight segments, an intermediate value can be estimated by linear interpolation. The estimate depends on that straight-line convention; it is not an additional listed observation.
Worked Example: Reading Listed Values and an Intermediate Estimate
A hypothetical workshop’s schedule gives the following weekly quantities:
| Price per item | Items supplied per week |
|---|---|
| $6 | 10 |
| $9 | 18 |
| $12 | 26 |
| $15 | 34 |
On a graph with quantity on the horizontal axis and price on the vertical axis, identify the quantity at $12 and the price at quantity 18. Then, if adjacent plotted points are connected by straight segments, estimate the price at quantity 22.
Method. The schedule entries become \((10,6)\), \((18,9)\), \((26,12)\), and \((34,15)\). At a vertical-axis value of $12, the corresponding point is \((26,12)\), so the quantity is 26 items per week. At horizontal-axis value 18, the point is \((18,9)\), so the price is $9 per item.
Quantity 22 lies between 18 and 26. Its position within that interval is:
The two endpoint prices are $9 and $12, a difference of \(12-9=\$3\). Halfway between those prices is:
Thus, under the stated straight-segment convention, the estimated price at quantity 22 is $10.50 per item. Without that convention, the schedule alone does not give an exact price at quantity 22.
Check. Quantity 22 is halfway from 18 to 26, and $10.50 is halfway from $9 to $12. The calculation avoids treating the intermediate estimate as a schedule entry.
Units and Scale Labels Matter
Sometimes an axis reports quantities in thousands rather than individual units. The coordinate is then interpreted in the units stated on that axis. For example, a horizontal coordinate of 8 on an axis labelled “Quantity supplied (thousand units per week)” means 8,000 units per week. It does not mean 8 individual units.
Likewise, a price may be quoted per item, per package, or per other unit. The vertical coordinate must be read with the full label. A point at vertical value 9 on an axis labelled “Price (dollars per package)” means $9 per package. Omitting units can make a numerically correct reading economically unclear or wrong.
Worked Example: Reading a Graph Measured in Thousands
A hypothetical packaging producer reports this schedule, where quantity is measured in thousands of cartons per week:
| Price per carton | Quantity supplied (thousand cartons per week) |
|---|---|
| $3 | 2 |
| $6 | 5 |
| $9 | 8 |
| $12 | 11 |
Plot the schedule with a horizontal axis marked in thousands of cartons and a vertical axis in dollars per carton. Then report the quantity at $9 and the price at a quantity of 5 thousand cartons.
Method. Because the horizontal axis is in thousands, use the displayed quantities directly as coordinates. The plotted pairs are \((2,3)\), \((5,6)\), \((8,9)\), and \((11,12)\), where the first coordinate is thousands of cartons and the second is dollars per carton. A horizontal scale from 0 to 12 thousand and a vertical scale from $0 to $12 cover all four entries.
At price $9, the point is \((8,9)\), so the graph shows 8 thousand cartons per week. Converting to cartons gives \(8\times 1{,}000=8{,}000\) cartons per week. At a quantity coordinate of 5 thousand cartons, the point is \((5,6)\), so the price is $6 per carton.
Check. Both readings match their schedule rows, and the first quantity has been converted from thousands to individual cartons. The method avoids reading “8” as 8 cartons when the axis specifies thousands.
Why the Coordinate Convention Works
A graph represents each schedule entry as a pair of values. The conventional ordered pair on a two-dimensional graph is written \((x,y)\), where \(x\) is the horizontal coordinate and \(y\) is the vertical coordinate. For a supply schedule, quantity is assigned to \(x\) and price to \(y\). Therefore an entry “quantity \(Q\) at price \(P\)” must be plotted as \((Q,P)\).
This also explains why a typical upward-sloping supply schedule appears to rise from left to right: when a schedule records a larger quantity at a higher price, both the horizontal coordinate and the vertical coordinate increase. The visual direction follows from the paired values and axis convention. The purpose of the graph is to preserve those values, not to replace them; checking the plotted points against the table is the most direct verification.
Common Graphing Traps
- Reversing the axes. A schedule row with quantity 7 at price $12 is plotted at \((7,12)\), not \((12,7)\). The first number belongs on the horizontal axis.
- Ignoring the scale. If each tick represents 5 units, a point halfway between two ticks is not at the next tick. Read the axis labels and intervals before estimating a coordinate.
- Dropping the unit. A quantity axis labelled in thousands makes a coordinate of 8 equal to 8,000 units, not 8 units.
- Inventing intermediate entries. A point between listed observations is not automatically an exact schedule value. Use interpolation only when the graph or question specifies a straight-line connection.
- Reading in the wrong direction. For a given price, begin on the vertical axis and travel to the schedule; for a given quantity, begin on the horizontal axis.
These checks are useful in any numerical graphing task: confirm the axes, confirm the scale, retain the units, and compare each coordinate with its original table entry. A supply graph that passes those checks communicates the schedule clearly and can be read without changing what the data say.
Check Your Understanding
For each problem, use quantity on the horizontal axis and price on the vertical axis.
- A schedule lists 4 boxes at $5, 9 boxes at $10, and 15 boxes at $15. Write the three ordered pairs and state the quantity supplied at $10. (Answer: \((4,5)\), \((9,10)\), \((15,15)\); 9 boxes.)
- A graph has a horizontal axis marked in equal intervals of 2 units and a vertical axis marked in equal intervals of $3. A plotted point is at horizontal value 8 and vertical value $12. State its ordered pair and interpret it in words. (Answer: \((8,12)\); quantity supplied is 8 units at a price of $12.)
- A schedule gives 3 thousand units at $4, 6 thousand units at $8, and 9 thousand units at $12. What quantity does the graph show at $8, both in thousands and in individual units? (Answer: 6 thousand units, or 6,000 units.)
- Two schedule entries are quantity 12 at $7 and quantity 20 at $11. If their plotted points are connected by a straight segment, estimate the price at quantity 16. (Answer: $9.)
- A point is plotted at \((14,9)\), and the axes are labelled “Quantity supplied (hundreds per week)” and “Price (dollars per unit).” State the weekly quantity in individual units and the price. (Answer: 1,400 units per week at $9 per unit.)