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*x-6*y-(3)=0 

Step  1  :

Pulling out like terms :

 1.1     Pull out like factors :

   -3x - 6y - 3  =   -3 • (x + 2y + 1) 

Equation at the end of step  1  :

Step  2  :

Equations which are never true :

 2.1      Solve :    -3   =  0

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

Equation of a Straight Line

 2.2     Solve   x+2y+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  x+2y+1  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

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

  y-intercept = -1/2  = -0.50000 

Calculate the X-Intercept :

When y = 0 the value of x is -1/1 Our line therefore "cuts" the x axis at x=-1.00000

  x-intercept = -1/1  = -1.00000 

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -0.500 and for x=2.000, the value of y is -1.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -1.500 - (-0.500) = -1.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     = -1.000/2.000 = -0.500 

Geometric figure: Straight Line

1.   Slope = -1.000/2.000 = -0.500
2.   x-intercept = -1/1 = -1.00000
3.   y-intercept = -1/2 = -0.50000