Conversion Graphs

Worked example

1. 1

   $25\text{ miles}$ — The question gives miles, so start on the miles axis and find 25.

2. 2

   $\uparrow \text{ to the line}$ — Go straight up from 25 until you meet the line. Every point on the line is a matching pair.

3. 3

   $\to 40$ — From that point go straight across to the km axis and read the value.

4. 4

   $25\text{ miles}=40\text{ km}$ — Write the answer with its unit. The answer is in km, because that is the axis you finished on.

Worked example

1. 1

   $90\text{ AUD}$ — The question gives Australian dollars, so start on the dollars axis and find 90.

2. 2

   $\to \text{ to the line}$ — Dollars are on the upright axis, so go straight across until you meet the line.

3. 3

   $\downarrow 64$ — From that point go straight down to the euros axis and read the value.

4. 4

   $90\text{ AUD}=64\text{ euros}$ — Write the answer with its unit. You finished on the euros axis.

Worked example

1. 1

   $(0,0)$ — 0 pounds is 0 euros, so the line starts at the origin.

2. 2

   $(25,30)$ — Plot the given pair: go along to 25 on the pounds axis and up to 30 on the euros axis. Mark a small cross.

3. 3

   $\text{ruled line through both}$ — Join the origin to your cross with a ruler. Carry the line on to the edge of the grid so you can read bigger amounts.

4. 4

   $50\text{ pounds}\to 60\text{ euros}$ — Check with a second point: 50 is 2 times 25, so the line must pass through 60 on the euros axis. If it does not, redraw.

Worked example

1. 1

   $200\text{ dirham}=47\text{ euros}$ — 200 is on the graph. Find it on the dirham axis, go across to the line, then down to the euros axis.

2. 2

   $400÷200=2$ — 400 dirham is 2 times as much as 200 dirham, so the euros will be 2 times as much too.

3. 3

   $2\times 47=94\text{ euros}$ — Multiply the euros by the same 2. This only works because the line starts at (0, 0).

4. 4

   $\text{other shop}=90\text{ euros}$ — Both prices are now in euros, the same unit, so we can compare them.

5. 5

   $90<94$ — 90 is less than 94.

6. 6

   $\text{France is cheaper}$ — The French price is smaller. Write both prices in your answer.

Worked example

1. 1

   $24÷0.75=32\text{ km}$ — The graph shows miles and km, not dollars. The fare is $24 and each km costs $0.75, so divide to find the km.

2. 2

   $32\text{ km}\to \text{to the line}$ — Find 32 on the km axis, which is the upright axis, and go straight across to the line.

3. 3

   $\downarrow 20\text{ miles}$ — Go straight down to the miles axis and read the value.

4. 4

   $20\times 1.6=32$ — Check: 20 miles should be 32 km, and it is.

Worked example

1. 1

   $30^{\circ }\text{C}=86^{\circ }\text{F}$ — Read the graph at 30 °C: go up to the line, then across to the °F axis.

2. 2

   $2\times 86=172$ — Try doubling, as you would on a line through zero. It gives 172.

3. 3

   $60^{\circ }\text{C}={140}^{\circ }\text{F}$ — Now read the graph itself at 60 °C. It gives 140, not 172, so doubling fails. The line does not start at 0.

Worked example

1. 1

   $0^{\circ }\text{C}=32^{\circ }\text{F}$ — A rise of 20 °C: read the graph at the start, 0 °C.

2. 2

   $20^{\circ }\text{C}=68^{\circ }\text{F}$ — Read the graph at the end of the rise: 0 + 20 = 20 °C.

3. 3

   $68-32={36}^{\circ }\text{F}$ — A rise is end minus start, so subtract the two readings.