0580

Real Life Graphs

Coordinate Geometry and Graphs

Flashcards

Reading a value off

  • Two quantities that are linked by a fixed rule can be plotted as one straight line, and that line is a conversion graph: either quantity can be found from the other
  • Typical pairs are kilometres and miles, litres and gallons, one currency and another, or a charge against the amount used
  • To convert, start on the axis holding the value you have, go across or up to the line, then turn and read the other axis
A conversion graph of cost in pounds against mass in kilograms, a straight line through the origin, used in both directions: an arrow up from 20 kg then left to £12, and an arrow left from £30 then down to 50 kg
Source: Conversion graphs by Save My Exams
  • Draw those two lines on the graph in pencil, because the examiner credits the reading and the working shows where it came from
A price-against-hours graph with a red line drawn across from £320 on the vertical axis to the line, then straight down to the horizontal axis to read off about 4.6 hours
Source: Conversion graphs by Save My Exams
  • Read the scale on each axis before anything else, since one square is very often not one unit

Graphs through the origin, and graphs that are not

  • A line through the origin means the two quantities are in direct proportion, so values can be scaled up
    • If 80 km reads as 50 miles, then 240 km is three times as far, giving 150 miles
  • A line that starts part way up the vertical axis has a fixed amount built in, and scaling then fails
    • A taxi charging £3 before it moves plus £2 for each mile starts at £3 and reaches £13 after 5 miles
A price-against-hours graph whose line meets the vertical axis at about £45 rather than at the origin, so there is a fixed charge before any hours are counted and values cannot simply be scaled up
Source: Conversion graphs by Save My Exams
  • That starting value is the fixed charge, read where the line meets the vertical axis
  • To convert a value beyond the printed grid on such a graph, find the equation of the line instead of scaling
Exam tip

Draw the two lines you used to take a reading, straight across and straight down, and leave them on the graph. A reading is marked against a range of acceptable values, so the lines are what show the examiner where your answer came from.

Worked example

Reading a conversion graph both ways

The graph converts between degrees Celsius and degrees Fahrenheit. Use it to convert 100 °F into °C, and 60 °C into °F.

A conversion graph with degrees Celsius from 0 to 100 along the bottom and degrees Fahrenheit from 0 to 250 up the side, crossed by a straight line from about (0, 32) to (100, 212); a red line runs across from 100 on the Fahrenheit axis to the line and then straight down to the Celsius axis
Source: Conversion graphs by Save My Exams

Solution:

  • For 100 °F, start on the vertical axis because Fahrenheit is the quantity given
  • Go across from 100 until the line is reached, then straight down to the Celsius axis
  • The reading is a little under 38, so 100 °F is about 37.5 °C
  • For 60 °C, start on the horizontal axis this time
  • Go up from 60 until the line is reached, then straight across to the Fahrenheit axis
  • The reading is 140 °F
  • The line does not pass through the origin: at 0 °C it is already at 32 °F, so these two scales cannot be converted by multiplying alone