Gallons 11 10 9 8 7 6 5 4 3 2 1 0 0 10 20 litres 30 40 50 The graph shows the relationship between litres and gallons. a) Convert 41 litres to gallons. b) Convert 3.5 gallons to litres.
The Correct Answer and Explanation is:
Answers:
a) Convert 41 litres to gallons:
From the graph, locate 41 litres on the x-axis. Trace vertically until you meet the blue line, then move horizontally to the y-axis to read the corresponding number of gallons.
➡️ 41 litres ≈ 9 gallons
b) Convert 3.5 gallons to litres:
Locate 3.5 gallons on the y-axis. Trace horizontally to the blue line, then drop down vertically to the x-axis to find the equivalent in litres.
➡️ 3.5 gallons ≈ 16 litres
Explanation
This graph illustrates the linear relationship between litres (x-axis) and gallons (y-axis). A straight line through the origin indicates a constant rate of conversion between the two units. When interpreting such a graph, the slope of the line represents the conversion factor. The steeper the slope, the more litres are required per gallon, or vice versa.
In question (a), we are given 41 litres and need to find the equivalent in gallons. By tracing the 41-litre mark upward until it intersects the blue line, and then moving leftward to the y-axis, we observe that 41 litres corresponds to approximately 9 gallons. This process reflects how a graph can convert between units without performing mathematical calculations.
In question (b), we start with 3.5 gallons on the y-axis. Tracing this across to the blue line and then down to the x-axis, we find that 3.5 gallons is roughly equal to 16 litres. This visual method is particularly useful for checking approximate conversions when precision to the decimal point is not required.
Mathematically, we can determine the conversion factor using known points. For example, from the graph:
50 litres = 11 gallons
So, the conversion factor from litres to gallons is 11 ÷ 50 = 0.22 gallons per litre.
And from gallons to litres: 50 ÷ 11 ≈ 4.55 litres per gallon.
These conversion factors verify our graph-based answers:
- 41 litres × 0.22 ≈ 9.02 gallons
- 3.5 gallons × 4.55 ≈ 15.93 litres
Thus, the graph provides an accurate visual tool for unit conversion based on proportional relationships.
