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 :

                     y-(-11*x-12)=0 

Step  1  :

Equation of a Straight Line

 1.1     Solve   y+11x+12  = 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  y+11x+12  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is -12/1 so this line "cuts" the y axis at y=-12.00000

  y-intercept = -12/1  = -12.00000 

Calculate the X-Intercept :

When y = 0 the value of x is -12/11 Our line therefore "cuts" the x axis at x=-1.09091

  x-intercept = -12/11  = -1.09091 

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 -12.000 and for x=2.000, the value of y is -34.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -34.000 - (-12.000) = -22.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     = -22.000/2.000 = -11.000 

Geometric figure: Straight Line

1.   Slope = -22.000/2.000 = -11.000
2.   x-intercept = -12/11 = -1.09091
3.   y-intercept = -12/1 = -12.00000