Slope and Intercepts in Real Life

Examples!

Thermal Expansion Problem:

The slope is -0.05 or . This means that the gap decreases 1 degree for every 20 degree increase in temperature.

(This is better than – “The slope is the change in gap size compared to temperature.”)

Shoe Problem:

The slope is 3. This means that the shoe size increases 3 sizes for every 1 inch the foot length increases.

The Cricket Problem: The slope is . This means that the chirping rate increases 8 chirps per minute for every 5 degrees that the temperature increases. (OR chirping rate increases 1.6 for every 1 degree increase in temperature)

(This is better than: “Slope is how much chirping changes compared to temperature.” STATE THE RATE OF CHANGE WITH THE NUMBERS AND THE CONTEXT)

INTERCEPTS:

Reaction Time Problem

The y-intercept is 4.2. Theoretically, when distance (x) is 0 cm, reaction time is 4.2 seconds. Therefore this 4.2 seconds must represent some sort of fixed reaction time in addition to the travel time (slope), because you will not have a distance of 0cm from the brain in a reasonable domain.

THE ELEVATOR PROBLEM

The x-intercept is Theoretically, if you have 0 feet of cable (y), the number of stories in your building would by But there is no such thing as negative stories in a building, so the x intercept is not in a reasonable domain for this problem.

THE MILK PROBLEM

X- Intercept ( What is x when y is zero?

The x- intercept is Theoretically, if you pay $0 you can buy quarts of milk. Ridiculous! Not in a reasonable domain for the problem.

Y-Intercept (0, 0.21) What is y when x is zero?

The y-intercept is 0.21. Theoretically, if you buy 0 quarts of milk you pay $0.21. Instead, this $0.21 probably represents a flat fee in addition to the per quart price. Perhaps a cost for the container, the label, or maybe delivery.