Rates of Change of Graphs Flashcards

All 5 cards in this deck

What does the gradient of a real-life straight line graph represent?

The rate of change of the y-quantity with respect to the x-quantity.
e.g. on a cost against units of electricity graph, the cost of each unit.

What are the steps to interpret the gradient of a real-life straight line graph?

e.g. cost in £ (y-axis) against units of electricity used (x-axis)

1. Gradient $=$ change in $y \div$ change in $x$
2. Give its units: £ per unit of electricity
3. Say it in context: the cost of each unit of electricity

What does the intercept on the vertical axis of a real-life graph represent?

e.g. a graph of volume $L$ litres against time $t$ seconds crosses at $L = 4$

The value of the y-quantity when $x = 0$ — the starting value.
Here: there were 4 litres in the container at the start.

True or false? On a graph of volume of petrol in a tank against distance travelled, a negative gradient means the car is slowing down.

False.
It means petrol is being used up as distance increases; the gradient is litres used per km.

What shape is the graph of time taken against speed for a fixed journey distance?

A reciprocal curve ($t = \frac{d}{s}$).
As speed increases the time falls, getting close to the axes but never touching them.