Straight Line Equation explained

Do you recall when your maths instructor spoke about the equation of a straight line in class? Same as me, you probably glanced out the window, silently deriding conventional schooling.

The teacher might have sparked a greater interest, had they suggested that learning this could eventually be beneficial to them financially.

Life can grant you a second chance, so take advantage of it. Pay attention and make the most of this opportunity; you might even profit from it!

The equation of a straight line reads something like this –

Y = mx + ε

For further information, click here to access a detailed explanation. Alternatively, you can keep reading for a simplified version.

Prior to delving into the equation, a brief remark on the symbols used –

y = Dependent variable

M = Slope

X = Independent variable

E = Intercept

The equation expresses that the value of y is contingent on x; multiplying x by its slope together with y and subsequently adding the intercept ‘e’ yields this value.

It seems complicated?

Let me give more detail on this. Before you ponder why we’re talking about straight line equations instead of relative value trading (RVT), don’t worry; this notion has a strong connection to RVT!

Imagine two fitness fanatics—FF1 and FF2. FF2 consistently surpasses FF1 in any challenge they take on. For example, if FF1 does 5 pushups, then FF2 will do 10, or if FF1 does 20 pull-ups, then FF2 will do 40. Below is a chart illustrating their pushup totals from Monday to Saturday.

If you were to guess how many push-ups FF2 will perform on Saturday, 30 would be your most straightforward answer.

The number of pushups FF1 does, determines how many FF2 will complete. FF1 just follows his body’s lead, but for FF2, the goal is twice as many pushups.

This makes FF2 a dependent variable and FF1 the independent one; in terms of the straight line equation, that would be FF2 = y and FF1 = x.

FF2 = FF1*M + ɛ

The equation can be translated into easy-to-understand language as follows:

FF2’s pushups are proportional to FF1’s, with a certain multiplier as well as an unchanging addition.

The slant of the line is indicated by the coefficient M, which has been determined to be 2, with a constant ɛ of 0. So the equation is –

FF2 = FF1*2 + 0

I trust the definition I posted is now clear. To reiterate, it reads:

Straight line equations assert that y, the dependent variable, can be calculated from its corresponding independent variable ‘x’, by multiplying x with its slope and adding the intercept ‘e’ to this outcome.

Now, think about another case 

These two hungry fellows, H1 and H2, have different appetites. Whereas H1 will cap off his meal at the prescribed amount of parathas, H2 can be relied upon to always finish an extra 1.5 for good measure – regardless of how full he is already feeling.

This table shows the total number of parathas consumed by two hungry individuals over the past six days.

H2 being incredibly hungry all the time, he eats twice as much as H1, plus an extra 1.5 parathas. This Saturday will be no different; he’ll be sure to gorge himself then too.

4*2 + 1.5 = 9.5 paratha!

Let us devise a linear equation for H1 and H2, just like we formulated for the healthy individuals. The quantity of parathas that H2 consumes is contingent on how many H1 eats — he will continue eating until he feels full.

H2 = H1*2 + 1.5

H2 is the dependent variable and its value is determined by H1. The slope is 2, with a constant of 1.5.

Let’s consider ‘Y’ to be a diet-conscious person. Every single day, whatever their hunger level, they stick to a strict 1.5 parathas only – neither more nor less.

So, X eats 3 paratha, Y eats 1.5, X eats 5, Y eats 1.5, X eats 2.5, Y eats 1.5. So on and so forth. So what do you think the equation states?

The equation ‘y = x*0 + 1.5’ can be expressed as ‘y = 1.5’.

The inclination here is 0, meaning that the value of y does not fluctuate with changes in x. Evidently, it stays at 1.5. Hopefully you now have an understanding of how two numerical sets can be correlated.

Forget about getting fit or eating parathas, here I will provide you with two sets of random numbers instead

X is the independent and Y is the dependent variable. Have you observed the relationship between these two? Yes, the relationship exists, its just not visible to the naked eye. 

To gain clarity, we must determine the values of the slope and constant ɛ. To do this, we must consider the relationship between the two.