Question

A straight line A passes through the points (0Ė32) and (5Ė41) .

A straight line B passes through the points (32Ė0) and (41Ė5) .
a) Find the equations of lines A and B in the form y = mx + c.
b) Find the point of intersection of lines A and B.
c) On the same pair of axes sketch the graphs of lines A and B, including the point of intersection.
What transformation links lines A and B?
d) If you are told that x in the equation for line A is degrees Celsius and y is degrees Fahrenheit,
and vice versa for line B, what can you deduce about the point of intersection.

Answer 1

Line A and B represent the relationship between Celsius and Fahrenheit. Therefore, the point of intersection represents a temperature at which Celsius and Fahrenheit are equal. This temperature is -40 degrees, the only temperature at which Celsius and Fahrenheit have the same numerical value.