Points on a graph in the first quadrant
Points on a graph in the first quadrant
In many situations one amount depends on another: the price depends on the weight, the distance on the time. The connection between the two amounts can be written in a table, and it can be seen in a graph – each column of the table is a point in the coordinate system.
A kilogram of apples costs 2 ₪.
| Weight (kg) | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Price (₪) | 0 | 2 | 4 | 6 | 8 | 10 |
Each column of the table is an ordered pair: (weight, price). For example, 3 kg cost 6 ₪ – the point .
We joined the apple points with a line, because you can buy any weight – kg too, and it costs 5 ₪: the point on the line has a meaning as well.
A bus ticket costs 3 ₪. Here we do not join the points: you cannot buy two and a half tickets, and the points in between have no meaning.
A candle 10 cm tall is burning: every hour it gets 2 cm shorter.
Complete a table of the candle’s height after 0, 1, 2, 3, 4 and 5 hours.
Draw the points in a coordinate system – the -axis for the hours and the -axis for the height.
Should you join them?
What happened after 5 hours?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Yoav went for a hike. The graph shows how many kilometres he had walked (the -axis) after each number of hours (the -axis). To find how far he had walked after one hour, find the point on the graph whose -coordinate is 1, and read its -coordinate: 4 km.
Answer from the hike graph: how far had Yoav walked after two hours?
After how long had he done 12 km?
What happened between the second hour and the third?
How many km did he walk in the last hour?
How far had he walked after half an hour – and how can you tell?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
In which of these situations do we join the points on the graph, and in which not? Explain.
a. The number of children in a class and the number of their shoes.
b. The time since planting and the height of the plant.
c. The amount of fuel put into a car (in litres) and the price paid for it.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power