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 :

                     10*t+15*b-(240)=0 

Step  1  :

Pulling out like terms :

 1.1     Pull out like factors :

   10t + 15b - 240  =   5 • (2t + 3b - 48) 

Equation at the end of step  1  :

Step  2  :

Equations which are never true :

 2.1      Solve :    5   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Equation of a Straight Line

 2.2     Solve   2t+3b-48  = 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  2t+3b-48  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when t = 0 the value of b is 16/1 so this line "cuts" the b axis at b=16.00000

  b-intercept = 48/3  =  16 

Calculate the X-Intercept :

When b = 0 the value of t is 24/1 Our line therefore "cuts" the t axis at t=24.00000

  t-intercept = 48/2  =  24 

Calculate the Slope :

Slope is defined as the change in b divided by the change in t. We note that for t=0, the value of b is 16.000 and for t=2.000, the value of b is 14.667. So, for a change of 2.000 in t (The change in t is sometimes referred to as "RUN") we get a change of 14.667 - 16.000 = -1.333 in b. (The change in b is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     = -1.333/2.000 = -0.667 

Geometric figure: Straight Line

1.   Slope = -1.333/2.000 = -0.667
2.   t-intercept = 48/2 = 24
3.   b-intercept = 48/3 = 16