Why would you ever need to know slope or rate of change in the real world?

Answer 1

The "slope" of the graph of any quantity tells how fast that quantity is changing.

Any quantity that changes in real life has a slope.

-- The slope of the car's odometer reading is the car's speed. That slope is so important

that a separate meter, called the "speedometer", is provided to show it.

-- The slope of the speedometer reading is the car's acceleration.

-- The slope of a road, track, or trail is called the "grade". Hikers and railroad drivers

always want to know the grade, because it tells them whether they'll be able to make it

past that piece of track or trail, and whether they'll need to get a running start.

-- People who build roads with curves have to be careful of what kind of slope they

build into the curves. If the slope of the pavement in a curve is wrong, then every

car on the curve flies off of the road.

-- Carpenters too. If the slope of the roof on a house or a building is wrong, then

the rain and snow don't run off fast enough, and the roof caves in.