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 :

                     3*a-2*b-(1)=0 

Step  1  :

Equation of a Straight Line

 1.1     Solve   3a-2b-1  = 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  3a-2b-1  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when a = 0 the value of b is 1/-2 so this line "cuts" the b axis at b=-0.50000

  b-intercept = 1/-2  = -0.50000 

Calculate the X-Intercept :

When b = 0 the value of a is 1/3 Our line therefore "cuts" the a axis at a= 0.33333

  a-intercept = 1/3  =  0.33333 

Calculate the Slope :

Slope is defined as the change in b divided by the change in a. We note that for a=0, the value of b is -0.500 and for a=2.000, the value of b is 2.500. So, for a change of 2.000 in a (The change in a is sometimes referred to as "RUN") we get a change of 2.500 - (-0.500) = 3.000 in b. (The change in b is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     =  3.000/2.000 =  1.500 

Geometric figure: Straight Line

1.   Slope = 3.000/2.000 = 1.500
2.   a-intercept = 1/3 = 0.33333
3.   b-intercept = 1/-2 = -0.50000