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 :

                     6*x+4*y-(58)=0 

Step  1  :

Pulling out like terms :

 1.1     Pull out like factors :

   6x + 4y - 58  =   2 • (3x + 2y - 29) 

Equation at the end of step  1  :

Step  2  :

Equations which are never true :

 2.1      Solve :    2   =  0

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

Equation of a Straight Line

 2.2     Solve   3x+2y-29  = 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  3x+2y-29  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 29/2 so this line "cuts" the y axis at y=14.50000

  y-intercept = 29/2  = 14.50000 

Calculate the X-Intercept :

When y = 0 the value of x is 29/3 Our line therefore "cuts" the x axis at x= 9.66667

  x-intercept = 29/3  =  9.66667 

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 14.500 and for x=2.000, the value of y is 11.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 11.500 - 14.500 = -3.000 in y. (The change in y 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.   x-intercept = 29/3 = 9.66667
3.   y-intercept = 29/2 = 14.50000