Straight-Line Graphs in Real Contexts – A14

Graphs III – AQA GCSE (8300): Higher Tier

In this course, Professor Keith Ball (University of Warwick) continues exploring graphs, covering Topics A14-A16 in the AQA GCSE (9-1) Mathematics (8300) Specification for Higher Tier. In the first mini-lecture, we learn about how straight-line graphs arise in real-world context, such as purchasing petrol or paying your plumber (Topic A14). In the second mini-lecture, we introduce distance-time graphs and discuss how the slope of such graphs corresponds to velocity at a particular time (Topic A14). In the third mini-lecture, we think more about velocity in distance-time graphs before considering velocity-time graphs and identifying the slope of such graphs as the acceleration (Topic A14). In the fourth mini-lecture, we learn about how exponential graphs model real-world processes like radioactive decay (Topic A14). In the fifth mini-lecture, we learn how to determine equations from exponential graphs (Topic A14). In the sixth mini-lecture, we shift gears to discussing the physical interpretations of gradients and areas under curves (Topic A15). In the seventh mini-lecture, we learn how to write the equations of circles (Topic A16) and in the eighth mini-lecture, we work with tangents of circles (Topic A16).

Straight-Line Graphs in Real Contexts – A14

In this mini-lecture, we introduce Topic A14 by exploring straight-line graphs in real contexts. In particular, we consider: (i) a graph depicting the cost of buying different amounts of petrol, from which we think about why the graph is a straight line and learn that the slope gives the cost per litre; (ii) the general principle that the slope of a graph is the rate at which the y variable changes with respect to the x variable; and (iii) a graph depicting the cost of a plumber with a call out charge, from which we see that this straight-line graph does not pass through the origin and that the y-intercept is the call out charge while the slope is the hourly rate.