Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "37.63" was replaced by "(3763/100)". 2 more similar replacement(s)

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                y-(-(221/100)*x+(3763/100))=0 

Step  1  :

            3763
 Simplify   ————
            100 

Equation at the end of step  1  :

               221          3763
  y -  ((0 -  (——— • x)) +  ————)  = 0 
               100          100 

Step  2  :

            221
 Simplify   ———
            100

Equation at the end of step  2  :

               221          3763
  y -  ((0 -  (——— • x)) +  ————)  = 0 
               100          100 

Step  3  :

Adding fractions which have a common denominator :

 3.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 -221x + 3763     3763 - 221x
 ————————————  =  ———————————
     100              100    

Equation at the end of step  3  :

       (3763 - 221x)
  y -  —————————————  = 0 
            100     

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  100  as the denominator :

          y     y • 100
     y =  —  =  ———————
          1       100  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 y • 100 - ((3763-221x))     100y + 221x - 3763
 ———————————————————————  =  ——————————————————
           100                      100        

Equation at the end of step  4  :

  100y + 221x - 3763
  ——————————————————  = 0 
         100        

Step  5  :

When a fraction equals zero :

 5.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

  100y+221x-3763
  —————————————— • 100 = 0 • 100
       100      

Now, on the left hand side, the  100  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   100y+221x-3763  = 0

Equation of a Straight Line

 5.2     Solve   100y+221x-3763  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  100y+221x-3763  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 3763/100 so this line "cuts" the y axis at y=37.63000

  y-intercept = 3763/100  = 37.63000 

Calculate the X-Intercept :

When y = 0 the value of x is 3763/221 Our line therefore "cuts" the x axis at x=17.02715

  x-intercept = 3763/221  = 17.02715 

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 37.630 and for x=2.000, the value of y is 33.210. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 33.210 - 37.630 = -4.420 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     = -4.420/2.000 = -2.210 

Geometric figure: Straight Line

1.   Slope = -4.420/2.000 = -2.210
2.   x-intercept = 3763/221 = 17.02715
3.   y-intercept = 3763/100 = 37.63000