methods 1 2 resources Maths Methods Questions

[methods 1 2 resources]

I always get confused for e.g i want to plot something on a graph,

 to find e.g 3y-8x=14, i use the x and y intercept method so 3y=14, but here is the QUESTION, e.g another question is 3x+3y=9, to find x its 3x=9, which is 3, but how come in the other question its 3/14 and not 14/3?

[lzxnl]

3/14? What is 3/14? The y intercept should be y=14/3...

[methods 1 2 resources]

3/14? What is 3/14? The y intercept should be y=14/3...

3 divided by 14, yea thats what I'm saying when a question is like 3x=9 its 3 but how come when you divide its not an even number for e.g 3x=14 its never 14 divided by 3 and its over 3 divided by 14???

[lzxnl]

What's the actual question? Intercepts of 3y-8x-14 and you want y intercepts? If so, your answers are wrong.

[pi]

3 divided by 14, yea thats what I'm saying when a question is like 3x=9 its 3 but how come when you divide its not an even number for e.g 3x=14 its never 14 divided by 3 and its over 3 divided by 14???

[methods 1 2 resources]

how do you graph

y=200x-1000?

[Stevensmay]

Two point method means that we want to find two co-ordinates that the line passes through.

Easiest way to do this is to make y = 0, find a co-ordinate which happens to be (5,0) because x = 5.
Then make x = 0, find a co-ordinate which is (0,-1000) because when x = 0, y = -1000.

Plot these two co-ordinates on your graph and simply draw a line that passes through both of them.

This will only work for linear graphs.

[methods 1 2 resources]

When giving two points e.g (2,1) and (3,4) i know how to work out m and put it into an equation mx+c.  But does it matter if i list the first points(2,1) as x1 and y1?  or does (3,4) have to be x1 and y1? does it matter? 

So my question to find m through two coordinates the formula is y2-y1 over x2-x1 does it matter which coordinates i label x1 or y1??? will i get the same answers?

Two point method means that we want to find two co-ordinates that the line passes through.

Easiest way to do this is to make y = 0, find a co-ordinate which happens to be (5,0) because x = 5.
Then make x = 0, find a co-ordinate which is (0,-1000) because when x = 0, y = -1000.

Plot these two co-ordinates on your graph and simply draw a line that passes through both of them.

This will only work for linear graphs.

isn't the x- and y-intercept method?

[Stevensmay]

isn't the x- and y-intercept method?

Which happens to be the same as the 'join the dots' method.

When giving two points e.g (2,1) and (3,4) i know how to work out m and put it into an equation mx+c.  But does it matter if i list the first points(2,1) as x1 and y1?  or does (3,4) have to be x1 and y1? does it matter? 

So my question to find m through two coordinates the formula is y2-y1 over x2-x1 does it matter which coordinates i label x1 or y1??? will i get the same answers?

Try it and find out?

[brightsky]

methods 1 2 resources, I've merged all the threads you created on this board so that all your questions are in one place.

As for your question, try not to memorize any formulas. It doesn't really matter what method you use, so long as you arrive at the correct answer. Although it might seem cool giving random names to random formulas, you will find that the more maths you do, the more unrealistic it becomes to simply label and memorize set formulas.

By definition, a linear function is a function of the form f(x) = ax + b, where a and b are real numbers. It just so happens that the gradient (which is a really bad word to use but it will suffice as far as VCE is concerned) of the line is a, and the y-intercept is b. So teachers prefer to teach students the formula y = mx + c, where m stands for gradient and c stands for y-intercept. While it may be useful to rote-learn this formula and plug in numbers to find m and c, it is much more beneficial for you to understand exactly what is going on behind the scenes.

Suppose we had a line on a set of axes. Suppose you were in a game show and you were asked to tell a friend just enough information so that he can work out the equation of the line and draw the line himself. What would you tell him? Is it sufficient just to tell to tell him one point on the line? No. There are billions of lines which pass through a single given point. Is it sufficient to tell him two points on the line? Yes! Just say you told him that the line passes through (1,2) and (3,4). No other line passes through BOTH these points. So given two points on the line, that friend of yours would be able to work out the equation of the line and sketch it himself. Suppose you didn't want to tell him two points on the line. What else can you tell him? Well, you can tell him the gradient of the line and one point on the line. He'll be able to work out the equation of the line. What else? You can also tell him the angle which the line makes with the positive direction of the x-axis and one point on the line. Again, he'll be able to work out the equation of the line. Now, what happens if you give him three points on the line? Well, he'll have MORE information than he needs to work out the equation of the line.

The above might sound a little silly, but it is crucial to understanding why all these different methods exist.

In general, to find the equation of a line:
1. Find the gradient of the line. (You should not just memorise (y2-y1)/(x2-x1). Understand WHY this is the formula. The gradient is defined as rise/run. That is a definition, no understanding needed. So how do you find out the rise? How do you find out the run? Sketch a line yourself, take two points and think. You should be able to work it out yourself.)
2. Shove it into the formula y - y1 = m (x - x1). (Again don't just memorise this formula. Understand WHY this is the formula. You are given that (x1,y1) is on the line. You also know the gradient is m. Why does that mean that the equation of the line is that? Again, you should be able to work that one out yourself with a little thinking.)
3. Rearrange if you so desire.

That is ALL you need to know to be able to find the equation of ANY line. Cast all the fancy names such as 'x-int and y-int formula', 'two point formula', 'one point formula', etc. out of your mind.

Hope this clears things up.

[methods 1 2 resources]

methods 1 2 resources, I've merged all the threads you created on this board so that all your questions are in one place.

As for your question, try not to memorize any formulas. It doesn't really matter what method you use, so long as you arrive at the correct answer. Although it might seem cool giving random names to random formulas, you will find that the more maths you do, the more unrealistic it becomes to simply label and memorize set formulas.

By definition, a linear function is a function of the form f(x) = ax + b, where a and b are real numbers. It just so happens that the gradient (which is a really bad word to use but it will suffice as far as VCE is concerned) of the line is a, and the y-intercept is b. So teachers prefer to teach students the formula y = mx + c, where m stands for gradient and c stands for y-intercept. While it may be useful to rote-learn this formula and plug in numbers to find m and c, it is much more beneficial for you to understand exactly what is going on behind the scenes.

Suppose we had a line on a set of axes. Suppose you were in a game show and you were asked to tell a friend just enough information so that he can work out the equation of the line and draw the line himself. What would you tell him? Is it sufficient just to tell to tell him one point on the line? No. There are billions of lines which pass through a single given point. Is it sufficient to tell him two points on the line? Yes! Just say you told him that the line passes through (1,2) and (3,4). No other line passes through BOTH these points. So given two points on the line, that friend of yours would be able to work out the equation of the line and sketch it himself. Suppose you didn't want to tell him two points on the line. What else can you tell him? Well, you can tell him the gradient of the line and one point on the line. He'll be able to work out the equation of the line. What else? You can also tell him the angle which the line makes with the positive direction of the x-axis and one point on the line. Again, he'll be able to work out the equation of the line. Now, what happens if you give him three points on the line? Well, he'll have MORE information than he needs to work out the equation of the line.

The above might sound a little silly, but it is crucial to understanding why all these different methods exist.

In general, to find the equation of a line:
1. Find the gradient of the line. (You should not just memorise (y2-y1)/(x2-x1). Understand WHY this is the formula. The gradient is defined as rise/run. That is a definition, no understanding needed. So how do you find out the rise? How do you find out the run? Sketch a line yourself, take two points and think. You should be able to work it out yourself.)
2. Shove it into the formula y - y1 = m (x - x1). (Again don't just memorise this formula. Understand WHY this is the formula. You are given that (x1,y1) is on the line. You also know the gradient is m. Why does that mean that the equation of the line is that? Again, you should be able to work that one out yourself with a little thinking.)
3. Rearrange if you so desire.

That is ALL you need to know to be able to find the equation of ANY line. Cast all the fancy names such as 'x-int and y-int formula', 'two point formula', 'one point formula', etc. out of your mind.

Hope this clears things up.

wait so for e.g plot y=2x-8.  this booklet says to use x and y intercept method but if i use the rise over run method the answers are different?  i thought you said it doesn't matter what method you use?

[Stevensmay]

wait so for e.g plot y=2x-8.  this booklet says to use x and y intercept method but if i use the rise over run method the answers are different?  i thought you said it doesn't matter what method you use?

I think you have completely missed what Brightsky was trying to say...

All methods will yield the same answer, for the equation does not change. It just happens that certain equations happen to be better suited to a different method, so we pick that method.

You can use just a single method for all linear equations, but it often means we will have to rearrange them, which can take time. Rather than doing this, we pick a different method (way of looking at it) that is more suited to the type of equation we have.

From a 'getting the correct answer' view, it does not matter what method we use.
From a 'how easy is it to get the answer' view, which method we use does matter. Some methods may be more complicated than others for a particular question, but they all yield the same answer.

[methods 1 2 resources]

I think you have completely missed what Brightsky was trying to say...

All methods will yield the same answer, for the equation does not change. It just happens that certain equations happen to be better suited to a different method, so we pick that method.

You can use just a single method for all linear equations, but it often means we will have to rearrange them, which can take time. Rather than doing this, we pick a different method (way of looking at it) that is more suited to the type of equation we have.

From a 'getting the correct answer' view, it does not matter what method we use.
From a 'how easy is it to get the answer' view, which method we use does matter. Some methods may be more complicated than others for a particular question, but they all yield the same answer.

so what should i do? should i know just one method or do i need to know all methods?

[Stevensmay]

You need to know and understand how all methods work.
Simply being able to apply them isn't enough, you need to know why method X works as it does.

[methods 1 2 resources]

You need to know and understand how all methods work.
Simply being able to apply them isn't enough, you need to know why method X works as it does.

but i don't understand

the question says using the 2 point method graph y=250x+300.  On a sac would it tell me which method to use cause if it didn't i would probably use the rise over sun method which i used but the answer is completely different to using the 2 point method, I'm confused???