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 :

                     x-1^2+y+6^2-(16)=0 

Step  1  :

 1.1     6 = 2•3

(6)² = (2•3)² = 2² • 3²

Equation at the end of step  1  :

  (((x -  (12)) +  y) +  (22•32)) -  16  = 0 

Step  2  :

Equation at the end of step  2  :

  x + y + 19  = 0 

Step  3  :

Equation of a Straight Line

 3.1     Solve   x+y+19  = 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+y+19  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is -19/1 so this line "cuts" the y axis at y=-19.00000

  y-intercept = -19/1  = -19.00000 

Calculate the X-Intercept :

When y = 0 the value of x is -19/1 Our line therefore "cuts" the x axis at x=-19.00000

  x-intercept = -19/1  = -19.00000 

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 -19.000 and for x=2.000, the value of y is -21.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -21.000 - (-19.000) = -2.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     = -2.000/2.000 = -1.000 

Geometric figure: Straight Line

1.   Slope = -2.000/2.000 = -1.000
2.   x-intercept = -19/1 = -19.00000
3.   y-intercept = -19/1 = -19.00000