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 :

                     4*x-6*y-(5)=0 

Step  1  :

Equation of a Straight Line

 1.1     Solve   4x-6y-5  = 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  4x-6y-5  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 5/-6 so this line "cuts" the y axis at y=-0.83333

  y-intercept = 5/-6  = -0.83333 

Calculate the X-Intercept :

When y = 0 the value of x is 5/4 Our line therefore "cuts" the x axis at x= 1.25000

  x-intercept = 5/4  =  1.25000 

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 -0.833 and for x=2.000, the value of y is 0.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 0.500 - (-0.833) = 1.333 in y. (The change in y 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.   x-intercept = 5/4 = 1.25000
3.   y-intercept = 5/-6 = -0.83333