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 :

                     r+s-(-12)=0 

Step  1  :

Equation of a Straight Line

 1.1     Solve   r+s+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  r+s+12  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

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

  s-intercept = -12/1  = -12.00000 

Calculate the X-Intercept :

When s = 0 the value of r is -12/1 Our line therefore "cuts" the r axis at r=-12.00000

  r-intercept = -12/1  = -12.00000 

Calculate the Slope :

Slope is defined as the change in s divided by the change in r. We note that for r=0, the value of s is -12.000 and for r=2.000, the value of s is -14.000. So, for a change of 2.000 in r (The change in r is sometimes referred to as "RUN") we get a change of -14.000 - (-12.000) = -2.000 in s. (The change in s 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.   r-intercept = -12/1 = -12.00000
3.   s-intercept = -12/1 = -12.00000