For a fixed proportional conversion, such as an example exchange rate, the graph is a straight line through the origin. Some conversions, such as Celsius to Fahrenheit, have a nonzero intercept.
A linear cost graph has a fixed charge (the y-intercept) plus a rate (the gradient). A taxi with £3 call-out and £2 per km: C = 2d + 3.
The gradient of a real-life graph is a rate: money per unit, or distance per time.
Distance–time graphs
For cumulative distance travelled against time, gradient gives speed. Cumulative distance never decreases.
Some journey graphs instead show distance from the start: a fall shows returning towards it, and speed is the gradient’s magnitude for straight-line motion.
A flat section shows a stop. Average speed uses total distance travelled divided by total elapsed time, including stops.
Travel, stop, then travel
Speed–time graphs
Speed is on the y-axis. Gradient = acceleration; a negative gradient is deceleration.
A flat line means constant speed.
The area under the graph = distance travelled. Split into triangles and rectangles/trapezia to find it.
Distance from speed and time
Other rates
On a graph of volume of water against time, the gradient is the rate of flow. A steeper curve means faster change.
Be careful with units: speed in m/s, acceleration in m/s².
Curved graphs
On a curved graph the rate changes: find the gradient at a point by drawing a tangent and calculating rise ÷ run.
投影片
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