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Learn to plot straight-line conversion graphs from data tables and read between points using interpolation, with clear steps, common mistakes, and practice tasks.
Conversion graphs turn a table of paired values into a straight line you can read. This lesson shows how to plot points accurately, draw the line, and interpolate values that fall between plotted points. You will use simple, checkable arithmetic and consistent units. All examples use hypothetical numerical values chosen for clarity; measure your own equipment if you adapt the tasks. The convention for plotting is: x-axis for the input unit, y-axis for the output unit, equal spacing on each axis, and points marked with small crosses. Letter styles and handwriting vary, so the rubric accepts any legible, consistent marking that matches the stated convention.
Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.
A conversion graph is a straight line through plotted pairs of values. Start by labelling the x-axis with the input unit and the y-axis with the output unit. Choose a scale that fits all your data and leaves room to read between points. Plot each pair as a small cross, then draw a straight line through the points using a ruler. If the points do not line up exactly, check your arithmetic before adjusting the line.
For example, suppose a table converts kilometres to miles: 0 km = 0 miles, 5 km = 3.1 miles, 10 km = 6.2 miles, and 15 km = 9.3 miles. Plot kilometres on the x-axis from 0 to 15 and miles on the y-axis from 0 to 10. The points lie on a straight line, so you can read values between them.
Interpolation means estimating a value that lies between two plotted points on the line. Find the input value on the x-axis, move vertically to the line, then horizontally to the y-axis. Read the output value as precisely as your scale allows. Because the line is straight, the estimate is proportional: halfway between two x-values gives a y-value halfway between their y-values.
For the kilometres-to-miles graph, to estimate 7 km, note that 7 km is between 5 km (3.1 miles) and 10 km (6.2 miles). The difference in x is 5 km and in y is 3.1 miles. Moving 2 km from 5 km is 2/5 of the way, so add 2/5 of 3.1 = 1.24 miles to 3.1, giving about 4.34 miles. Reading from the graph should agree with this calculation within your scale's precision.
Accuracy depends on your scale and how carefully you plot. Use equal spacing on each axis and label every major tick. If a reading falls between two grid lines, estimate to the nearest half-division and say so. Do not invent printer tolerances or hardware standards; measure your actual ruler or grid if precision matters. Any numerical values in this lesson are hypothetical examples, not manufacturing specifications.
A quick check is to compare your graph reading with a simple proportion. For a straight line through the origin, the ratio output/input is constant. If your table gives 10 km = 6.2 miles, then 1 km is about 0.62 miles, so 7 km is about 4.34 miles. If your graph reading is far from this, recheck the plotting or the scale.
A table converts litres to gallons: 0 L = 0 gal, 10 L = 2.2 gal, 20 L = 4.4 gal, 30 L = 6.6 gal. Plot the graph and estimate 25 L in gallons.
About 5.5 gallons.
Why: Plot litres on the x-axis from 0 to 30 and gallons on the y-axis from 0 to 7. The points lie on a straight line. 25 L is halfway between 20 L (4.4 gal) and 30 L (6.6 gal). Halfway in y is (4.4 + 6.6)/2 = 5.5 gal. A proportional check: 25/10 × 2.2 = 5.5 gal.
A table converts kilograms to pounds: 0 kg = 0 lb, 2 kg = 4.4 lb, 4 kg = 8.8 lb, 6 kg = 13.2 lb. Using a straight-line graph through these points, estimate 5 kg in pounds.
About 11.0 lb.
Why: 5 kg is halfway between 4 kg (8.8 lb) and 6 kg (13.2 lb). Halfway in y is (8.8 + 13.2)/2 = 11.0 lb. Proportional check: 5/2 × 4.4 = 11.0 lb.
Check: Confirm the midpoint calculation and compare with the ratio 4.4 lb per 2 kg, which gives 2.2 lb per kg; 5 × 2.2 = 11.0 lb.
A table converts hours to minutes: 0 h = 0 min, 1 h = 60 min, 2 h = 120 min, 3 h = 180 min. Using the straight line, estimate 2.5 h in minutes.
150 minutes.
Why: 2.5 h is halfway between 2 h (120 min) and 3 h (180 min). Halfway is (120 + 180)/2 = 150 min. Proportional check: 2.5 × 60 = 150 min.
Check: Multiply the input by 60 minutes per hour and confirm it matches the midpoint reading.
A table converts metres to feet: 0 m = 0 ft, 1 m = 3.3 ft, 2 m = 6.6 ft, 3 m = 9.9 ft. Using the straight line, estimate 2.4 m in feet.
About 7.92 ft.
Why: 2.4 m is 0.4 of the way from 2 m to 3 m. The y-change is 9.9 − 6.6 = 3.3 ft. Add 0.4 × 3.3 = 1.32 ft to 6.6 ft, giving 7.92 ft. Proportional check: 2.4 × 3.3 = 7.92 ft.
Check: Compute 2.4 × 3.3 and compare with the interpolation result; both should be 7.92 ft.
A table converts US dollars to euros: 0 USD = 0 EUR, 10 USD = 9 EUR, 20 USD = 18 EUR, 30 USD = 27 EUR. Using the straight line, estimate 15 USD in euros.
13.5 EUR.
Why: 15 USD is halfway between 10 USD (9 EUR) and 20 USD (18 EUR). Halfway is (9 + 18)/2 = 13.5 EUR. Proportional check: 15 × 0.9 = 13.5 EUR.
Check: Use the ratio 9 EUR per 10 USD, i.e. 0.9 EUR per USD, and multiply by 15 to confirm 13.5 EUR.
Interpolation is estimating a value between two plotted points by reading the straight line at that input. Because the line is straight, the estimate is proportional to the distance between the points.
No. You can plot and read directly from the graph. A proportional check helps verify your reading, but writing an equation is outside this task's boundary.
Read to the nearest half-division of your scale and state that precision. Compare with a proportional calculation to catch large errors.
Recheck each pair against the table and your arithmetic. Small plotting errors are common; correct them before drawing the line.