Solution - Properties of a straight line

Step  1  :

Equation of a Straight Line

 1.1     Solve   g-f  = 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  g-f  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

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

  f-intercept = 0/-1  = -0.00000 

Calculate the X-Intercept :

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

  g-intercept = 0/1  =  0.00000 

Calculate the Slope :

Slope is defined as the change in f divided by the change in g. We note that for g=0, the value of f is 0.000 and for g=2.000, the value of f is 2.000. So, for a change of 2.000 in g (The change in g is sometimes referred to as "RUN") we get a change of 2.000 - 0.000 = 2.000 in f. (The change in f is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

     Slope     = 1

Geometric figure: Straight Line

1.   Slope = 1
2.   g-intercept = 0/1 = 0.00000
3.   f-intercept = 0/-1 = -0.00000