Melody

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Melody  Feb 11, 2022
 #1
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Oct 26, 2015
 #5
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Hi Thalys,

Omi67's answers are excellent.

I will just reiterate.

I might use a different example :/

 

 

Both yours are  the equation of lines.

Lines are oftenpresented in the form   

y=mx+b      (This is called gradient and y intercept form of a line)

m and b are just numbers.

for example    y=3x-6

In this example   m=3 and b=-6     (it is -6 because you added -6       y=3x+-6)

Now if you were going to find the y intercept in this example you could put x=0

and you would get  

y=3*0-6

y=-6

See how the tacked on "-6" IS the y intercept.   It always works this way.  

The tacked on "b" IS the y intercept.

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Now slope is another name for gradient.

\(gradient (slope) =\frac{rise}{run}\)

 

I was going to do a whole lot more but I might leave it for the moment.

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The gradient is given by the number in front of the x (this is the co-efficient of x)

In this example  the number in front of x is 3  SO the slope(gradient) is 3

 

I could have written my line as 

y= -6+3x 

This is back to front.  I want the lots of x first so I am going to rearrange it.

y = -6     +3x

the terms are -6    and   +3x      

I need them the other way around

                      +3x     and    -6

SO my equations is better written as

y=+3x-6

y= 3x-6

this is now in gradient and y intercept form      y=mx+b

b, the y intercept, is -6

and 

m, the gradient (slope) is  +3

 

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In your example  a)

y=  100      -15x

it is written back to front

you need to put the lots of x first.  Remember that there is an invisable + in front of the 100

y = +100    -15x

y=     -15x   +100

The y intercept is the number tacked on the end, it is usually given the letter b and it is  100

The gradient is given the letter m and it is  -15

 

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You should be able to do b yourself now :))

 

 

 

 

 

 

(b). A(t) = 150000 - 300t 

Oct 26, 2015