Read a straight-line graph
A coordinate is an ordered pair: horizontal input first, vertical output second. A graph can support forward readings, reverse readings and signed changes. A model prediction is limited by its known interval and physical meaning
- Identify and convert Read both axis titles and scales. Convert a physical quantity to graph units before substituting it as y
- Read forwards or backwards From x, trace vertically to the line then horizontally to y. From y, reverse this route
- Check the interval Between known observations is interpolation. Beyond them is extrapolation, even if the input is still visible within the graph window
- Calculate a change Subtract the earlier value from the later value. A difference between percentages is measured in percentage points
Worked example
A line has the graph rule shown below. Each vertical graph unit represents 10 L, and the known time interval is 1 to 3 minutes. When would the model give 90 L?
- \(\displaystyle y=90/10=9\)Convert litres to graph units
- \(\displaystyle x=(9-1)/2=4\)Read backwards by rearranging the rule
- \(\displaystyle 4>3\)The model gives 90 L at 4 minutes, beyond the known interval. This assumes the linear model continues and remains physically possible
Common mistakes
Difficulty levels
Questions about this topic
Are x and y always time and height?+
No. x is conventionally horizontal and y vertical, but their meanings and units depend on the axis titles
Is an endpoint interpolation?+
An endpoint is a known boundary value. Strict interpolation concerns values between known observations; extrapolation goes beyond them
Does a wider graph window change interpolation into extrapolation?+
No. Use the stated known interval. Enlarging the window does not create observations. Practice here explicitly treats its drawn segment as the known interval
How do I reverse a scaled graph reading?+
Convert the stated output into graph units first, then read horizontally to the line and down to the input axis
Is a falling line a negative quantity?+
Not necessarily. A positive quantity can decrease. Its signed change is negative even while both endpoint values remain positive
Can I always keep extending a straight line?+
No. Check whether the same process continues and whether the result respects bounds such as zero, 100% or capacity
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 10 Mathematics, chapter 6: Linear graphs