Bridges on highways often have expansion joints, which are small gaps in the roadway
between one bridge section and the next. The gaps are put there so the bridge will have room to
expand when the weather gets hot. Suppose a bridge has a gap of 1.3 cm when the temperature
is 22°C, and that the gap narrows to 0.9 cm when the temperature warms to 30°C. Assume the
gap width varies linearly with the temperature.
a) Write the particular equation for gap width (w) in terms of temperature (t).
b) How wide would the gap be at 35°C? At -10°C?
c) Plot the graph of this linear function. Use a suitable domain and label the horizontal and
vertical axis.
d) At what temperature would the gap close completely? What mathematical name is given
to this temperature?
e) What is the width-intercept? What does this tell you in the real world?
f) What is the slope? What does this number represent?