View Full Version : Quick! Help me, Math!

:p I just so happened that I(like half the rest of the class.) haven't completely gotten what the teacher explained today in class... :S

I need help! Any one good at math;

4. Find the slope of the line y=2x+3

Well folks, it's 8th grade algebra, and most of you should know it.... :p TEST YOUR KNOWLEDGE! :vlol: :D Perhaps do an explanation in paint? It would be really appreciated. :hug:

A line always has the general form:

y = m * x + n

Now, the slope is how much y will increase if you increase x by one. I could tell you, but it might be better if you find out for yourself. Hint: You might try just setting any number for X, and then setting the same number plus one for X, and compare the different Y's you get. Sorry, no paint from me, I don't have it on my computer.

xcrushterx

20-09-07, 17:56

Gradient is 2. Line cuts the Y-axis at (0,3)

Need me to draw the graph?

A line always has the general form:

y = m * x + n

Now, the slope is how much y will increase if you increase x by one. I could tell you, but it might be better if you find out for yourself. Hint: You might try just setting any number for X, and then setting the same number plus one for X, and compare the different Y's you get. Sorry, no paint from me, I don't have it on my computer.

Thank you Cochrane, it's a bit less foggy now. :hug:

Daniel (was it? :p): Stop making me feel stupid. :p

xcrushterx

20-09-07, 17:59

Crushter: Stop making me feel stupid. :p

I'm not :p

I'm being serious... want me to. It'll only take a sec.

I'm not :p

I'm being serious... want me to. It'll only take a sec.

No thank you.

xcrushterx

20-09-07, 18:00

No thank you.

Ok :)

I'll try my best to explain...

The 2x part is indeed the gradient - how steep the slope is. Kind of like what angle it's in.

The +3 is just basically whereabouts this line is. The steepness of the slope is the same no matter what this number is, but where it's placed on the graph is affected.

So if x = 2, then 2 x 2 + 3 = 7. On your graph, you can plot down the co-ordinates (2, 7). Then just find another number for x and do the same, then plot it down and then connect the lines to draw a slope!

Forgive me if it's wrong...:2

A line always has the general form:

y = m * x + n

Now, the slope is how much y will increase if you increase x by one. I could tell you, but it might be better if you find out for yourself. Hint: You might try just setting any number for X, and then setting the same number plus one for X, and compare the different Y's you get. Sorry, no paint from me, I don't have it on my computer.

Hmm, Check if I'm wrong then: Say X=9:

then:

y=2(9)+3

y=21

Then: (9,21)? >.> I hate algebra...

Cho: That's what I do, but how do I CHECK if it's right?

Yeah. And I love algebra because I always get the questions right in the test papers! xD

Here's a tedious method:

Substitute numbers in place of 'x'. For example, if you substitute in '1', you're left with '(2 * 1) + 3', which is basically '2 + 3', which is obviously 5. Therefore, when 'x' = 1, 'y' = 5. Now you subtitute 'x' with '2', giving you '(2 * 2) + 3', which is '4 + 3', which is 7, so when 'x' = 2, 'y' = 7. Now try it with '3'. (2 * 3) + 3 = 6 + 3 = 9, therefore when 'x' = 3, 'y' = 9. Finally I'd try it with 4. (2 * 4) + 3 = 8 + 3 = 11, therefore when 'x' = 4, 'y' = 11. Now we can look for a pattern. When 'x' = 1, 'y' = 5. When 'x' = 2, 'y' = 7. When 'x' = 3, 'y' = 9. When 'x' = 4, 'y' = 11. 5, 7, 9, 11. Notice a pattern? I thought you did. With this you can plot points on the graph. Assuming 'x' is along the bottom and 'y' is up the side, you can draw the coordinates (1,5), (2,7), (3,9) and (4,11) on the graph. With this you can clearly see that it's a straight line and can guess where it's going to go next. You should be able to see that the gradient is 2 because the line goes up 2 for every 1 it goes across.

You're lucky there's no indices involved, because that gives you curved lines. :cln:

Choose 2 values for x, and then find the values of y.

For example, x = –1, you get y = 2(–1) + 3 = -2 + 3 = 1.

For example, x = 2, I get y = 2(2) + 3 = 4 + 3 = 7.

Then the points (–1, 1) and (2, 7) are on the line y = –2x + 3. The slope of the line is:a = 1 -(7) = -6 = +2.

-1-(2) -3

Although you should know that the value before x is usually the slope. So you could find it immediately; unless they ask you for the entire process.

xcrushterx

20-09-07, 18:12

Quick way to draw the graph:

The Y-intercept is 3, so plot your first point at (0,3).

The gradient it 2, which is the same as 2/1.

So you go (from 0,3) up 2, and along 1, plot a point there and continue.

However, if the gradient is negative, you have to go up 2 and along the other way one, or down so and along the positive way one.

Choose 2 values for x, and then find the values of y.

For example, x = –1, you get y = 2(–1) + 3 = -2 + 3 = 1.

For example, x = 2, I get y = 2(2) + 3 = 4 + 3 = 7.

Then the points (–1, 1) and (2, 7) are on the line y = –2x + 3. The slope of the line is:a = 1 -(7) = -6 = +2.

-1-(2) -3

Although you should know that the value before x is usually the slope. So you could find it immediately; unless they ask you for the entire process.

Thanks Anubis, I think I get it now. :D

Just for fun, you can do it way more complicated, too: For any kind of function, you can create a second function that will give you the slope it has at any point. y = x^2, for example, draws a parable, which has a different slope everywhere. But you can get the slope at any particular point by finding the function which will give you the slope. Important rules here are that you reduce the exponent by 1 and multiply by the old value of the exponent, factors stay and constant summands turn to zero. Applied to y = x^2, this will give you y = 2x. Your question, y = 2x + 3, can also be written as y = 2 * x^1 + 3. If we apply the rules from above, we end up with y = 2*x^0 + 0, which can be simplified to y = 2. This function has no x, which means that the lines has the same slope everywhere (which should be obvious).

If none of this made any sense to you, don't worry, you're not supposed to know that (yet) anyway.

Thank you but no more fun than it already is please. :vlol:

Since it's from last year, but...

This one is set up like this :

y = ax +b

You already know

y=2x+3

"a" always tells you the slope.

y=ax+b

y=2x+3

So, a = 2 :)

I dont think I need to throw in my 2-cents on this one... You guys nailed it! :tmb:

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