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 :

                     p-(-3*q+1)=0 

Step  1  :

Equation of a Straight Line

 1.1     Solve   p+3q-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  p+3q-1  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when p = 0 the value of q is 1/3 so this line "cuts" the q axis at q= 0.33333

  q-intercept = 1/3  =  0.33333 

Calculate the X-Intercept :

When q = 0 the value of p is 1/1 Our line therefore "cuts" the p axis at p= 1.00000

  p-intercept = 1/1  =  1.00000 

Calculate the Slope :

Slope is defined as the change in q divided by the change in p. We note that for p=0, the value of q is 0.333 and for p=2.000, the value of q is -0.333. So, for a change of 2.000 in p (The change in p is sometimes referred to as "RUN") we get a change of -0.333 - 0.333 = -0.667 in q. (The change in q is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     = -0.667/2.000 = -0.333 

Geometric figure: Straight Line

1.   Slope = -0.667/2.000 = -0.333
2.   p-intercept = 1/1 = 1.00000
3.   q-intercept = 1/3 = 0.33333