# Thread: Learing variations of the same equations

1. ## Learing variations of the same equations

I'm workig through this book I have and an entire chapter is dedicated to y=mx+b equations. I've learnt a few ways of how to work out the graph. Also the book is teaching me a few different ways in which the equation can be structured. It's getting a bit monotonous and I'm bored of this stuff now. The problem is how important is this stuff? I mean I can graph any of the equations from the book but now it's showing me how to find the x and y interceps when they equation is in the form

$\displaystyle \frac{x}{a} + \frac{y}{b} = 1$ where the x and y intercep is b.

I really can't be bothered to keep going through all these varies methods, when I come to higher mathematics, will I come across this equation in many many different forms and is it worth learning them all?

2. ## Re: Learing variations of the same equations

Originally Posted by uperkurk
I'm workig through this book I have and an entire chapter is dedicated to y=mx+b equations. I've learnt a few ways of how to work out the graph. Also the book is teaching me a few different ways in which the equation can be structured. It's getting a bit monotonous and I'm bored of this stuff now. The problem is how important is this stuff? I mean I can graph any of the equations from the book but now it's showing me how to find the x and y interceps when they equation is in the form
$\displaystyle \frac{x}{a} + \frac{y}{b} = 1$ where the x and y intercep is b.
I really can't be bothered to keep going through all these varies methods, when I come to higher mathematics, will I come across this equation in many many different forms and is it worth learning them all?
YES! Skipping any topic in your systemic study of mathematics is done at great risk.
The basics are all important. That is why a complete course of mathematics study takes so long to complete. It is also the reason more students do not try to do it.

3. ## Re: Learing variations of the same equations

I understand... it's just getting a bit too much, every topic I'm learning I have to learn 6 different ways to work out the equations depending on their formats. I'm never going to remember them all a year down the line when I've moved on to more advanced topics such as calculus.

4. ## Re: Learing variations of the same equations

Originally Posted by uperkurk
I understandI'm never going to remember them all a year down the line when I've moved on to more advanced topics such as calculus.
Of course you will remember them if you keep using them over and over again.
That is the point of repeating and repeating.

5. ## Re: Learing variations of the same equations

$$p$$

6. ## Re: Learing variations of the same equations

Hello, uperkurk!

I went through the same resentment many years ago.

I was taught that there were four formulas to learn,
. . depending on what we are given.

[1] Slope-Intercept Formula: .$\displaystyle y \:=\:mx + b$
. . .in case you are given the slope $\displaystyle m$ and the y-intercept $\displaystyle b.$

[2] Two-Point Formula: .$\displaystyle y \:=\:\frac{y_2-y_1}{x_2-x_1}(x-x_1)$
. . .in case you are given two points: $\displaystyle (x_1,y_1)$ and $\displaystyle (x_2,y_2).$

[3] Point-Slope Formula: .$\displaystyle y - y_1 \:=\:m(x-x_1)$
. . .in case you are given the slope $\displaystyle m$ and a point $\displaystyle )x_1,y_1).$

[4] Two-Intercept Formula: .$\displaystyle \frac{x}{a} + \frac{y}{b} \:=\:1$
. . .in case you are given the x-intercept $\displaystyle a$ and the y-intercept $\displaystyle b.$

When I began teaching, I found this list highly annoying.
Then I "discovered" that we can get away with one formula.

First, we must know the Slope Formula.

Given two points: .$\displaystyle P(x_1,y_1),\;Q(x_2,y_2)$
. . the slope of the line through $\displaystyle P$ and $\displaystyle Q$ is: .$\displaystyle m \:=\:\frac{y_2-y_1}{x_2-x_1}$

Then we can always apply [3] the Point-Slope Formula: .$\displaystyle y - y_1 \:=\:m(x-x_1)$

We don't need [1].
If we are given the slope $\displaystyle m$ and the y-intercept $\displaystyle b$,
. . recall that the y-intercept is a point $\displaystyle (0,b).$
Substitute them into [3].

We don't need [2].
If we are given two points $\displaystyle P(x_1,y_1)$ and $\displaystyle Q(x_2,y_2)$
. . use the Slope Formula to find $\displaystyle m.$
. . Use either of the two points.
Substiture them into [3].

We don't need [4].
If we are given the two intercepts $\displaystyle (a,0)$ and $\displaystyle (0,b)$
. . use the Slope Formula to find $\displaystyle m.$
. . Use either of the two points.
Subsitute them into [3].

See? .All we need is the Point-Slope Formula.