Solution - Properties of a straight line

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "y1"   was replaced by   "y^1".  1 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 :

                     x^2/x^1-(y^2/y^1)=0 

Step  1  :

            y2
 Simplify   ——
            y 

Dividing exponential expressions :

 1.1    y² divided by y¹ = y^{(2 - 1)} = y¹ = y

Equation at the end of step  1  :

  (x2)    
  ———— -  y  = 0 
  (x1)    
 Step  2  :
            x2
 Simplify   ——
            x 

Dividing exponential expressions :

 2.1    x² divided by x¹ = x^{(2 - 1)} = x¹ = x

Equation at the end of step  2  :

  x -  y  = 0 

Step  3  :

Equation at the end of step  3  :

  x - y  = 0 

Step  4  :

Equation of a Straight Line

 4.1     Solve   x-y  = 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  x-y  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 0/-1 so this line "cuts" the y axis at y=-0.00000

  y-intercept = 0/-1  = -0.00000 

Calculate the X-Intercept :

When y = 0 the value of x is 0/1 Our line therefore "cuts" the x axis at x= 0.00000

  x-intercept = 0/1  =  0.00000 

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 0.000 and for x=2.000, the value of y is 2.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 2.000 - 0.000 = 2.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

     Slope     = 1

Geometric figure: Straight Line

1.   Slope = 1
2.   x-intercept = 0/1 = 0.00000
3.   y-intercept = 0/-1 = -0.00000