Solution - Properties of a straight line

Rearrange:

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

                     5*a-(w)=0 

Step  1  :

Equation of a Straight Line

 1.1     Solve   5a-w  = 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  5a-w  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

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

  w-intercept = 0/-1  = -0.00000 

Calculate the X-Intercept :

When w = 0 the value of a is 0/5 Our line therefore "cuts" the a axis at a= 0.00000

  a-intercept = 0/5  =  0.00000 

Calculate the Slope :

Slope is defined as the change in w divided by the change in a. We note that for a=0, the value of w is 0.000 and for a=2.000, the value of w is 10.000. So, for a change of 2.000 in a (The change in a is sometimes referred to as "RUN") we get a change of 10.000 - 0.000 = 10.000 in w. (The change in w is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

     Slope     = 5

Geometric figure: Straight Line

1.   Slope = 5
2.   a-intercept = 0/5 = 0.00000
3.   w-intercept = 0/-1 = -0.00000