Slope (as in $y = mx+b$) as it pertains to daily usage

Question

EDIT: I should've been more specific. I was hoping for feedback as it pertains to internet usage. More so, if I search something, anything, does the coding within that apply the use of Slope?

I know this is an odd request, but I got into a debate today as to if/how we use SLOPE daily. I was wondering if there was any way, by way of just searching anything on the internet, that slope is used. I argued that computationally there HAS to be slope somewhere involved within the coding process of search engines. Wether its as far off as: when you search $X$, that engine uses $Y$ theory which in turn uses $Z$ theory which slope is fundamental in (or a part of). Can anyone help or point me in the correct direction?

Answer 1

One's wages per hour would be the slope of the line used for their income over time (assuming they are paid at an hourly rate).

Another common usage is in linear approximations (if you've taken calculus, you've probably been asked to approximate something like $\sqrt{9.01}$ using linear approximations which boils down to looking at lines tangent to the curve and using the slope of the line).

Answer 2

This is an odd question because I'm having a hard time thinking of a place where linear functions aren't used in real life. Slope appears any time a line appears, which happens whenever two things are proportional.

• supply and demand (usually modeled with lines)
• velocity of a car with fixed acceleration
• all computer science is based on linear algebra
• battery charge is probably linear with time
• the gravitational potential energy of an object is linear with its vertical height
• time is linear
• the position of any object with constant velocity (cars on highway, objects in space)
• more generally, any "smooth" process can be estimated with lines, which, again, is sort of why they pop up almost everywhere.
• I believe crickets chirp at a rate which is linear with temperature
• Celcius and Fahrenheit are linearly related (although this is perhaps arbitrary)

There is a joke that the goal of all math is to reduce a complicated problem into linear algebra since that is the only field that is well understood.

Answer 3

The This Old House web site has instructions for measuring the slope of a roof:

https://www.thisoldhouse.com/ideas/determining-roof-pitch

To summarize, you measure the difference in the height of the roof at two places that are exactly $12$ inches apart in the horizontal dimension (not at a slant distance of $12$ inches). This gives you the same kind of "rise" and "run" measurements that many of us learned to apply to the graph of a line in high school math.

The slope of a roof is traditionally called "pitch" and its units are expressed in quaint terms such as "$6$-in-$12$," but they translate to a simple numeric slope: $$ 6\text{ in }12 = \frac{6}{12} = \frac12. $$

Even "flat" roofs generally have a slope (though a very gentle one) so that not too much water accumulates in pools.

So if you live in a building with a roof, you use slope every day, thanks to the architect, carpenters, and/or other builders who built that roof with a suitable slope.