A C T I V I T I E S How to inter pret g raphs The shape of a g raph shows the relat ionsh ip bet ween the va r iables represented . Somet imes it can be w r it ten w ith a mathemat ica l formu la . The price of different amounts of sweets: The price of the sweets is directly proportional to the amount: double the number of sweets is double the cost. • Directly proportional quantities • Mathematically: y = k ? x or x y k = The price of a container and different amounts of detergent: The price is proportional to the amount of detergent, but the container on its own has a cost (n) that is not zero. • Mathematically: y = k ? x + n, where n is the value of y when x is 0. Ascending straight line passing through the origin Ascending straight line not passing through the origin Parabolic curve The distance travelled by an object in free fall compared to the time taken. The distance is not proportional to the time. • Mathematically: y = k ? x2 The change in temperature of a liquid when it is placed inside a fridge: The decrease in temperature is directly proportional to time. It decreases 3 °C every two minutes. • Directly proportional quantities with a negative constant • Mathematically: y = -k ? x + n The pressure (p) of a gas when the volume of its container is changed, if the temperature is constant: The pressure of the gas is inversely proportional to its volume: the greater the volume, the lower the pressure. • Inversely proportional quantities • Mathematically: y ? x = k Descending straight line Rectangular hyperbolic curve If the time is doubled, the distance travelled is more than doubled. 12 Which type of graph would be made by the data in each of these tables? a) b) Variable 1 1 2 3 4 Variable 2 1.5 2.0 2.5 3.0 Variable 1 0 2 4 6 8 10 Variable 2 20 17 14 11 8 5 1 Price (€) Amount (L) 3 2 1 0 0 1 2 3 4 p (atm) V (L) 6 3 0 0 10 20 30 T (°C) t (min) 20 10 0 0 2 4 6 8 10 n is the value of y when x is 0. If there are no sweets, the cost is zero. Price (€) Sweets 3 2 1 0 0 100 200 300 400 d (m) t (s) 80 60 40 20 0 0 1 2 3 4 17
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