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 :

                     h-(-16*t*(2)+28*t+8)=0 

Step  1  :

Equation of a Straight Line

 1.1     Solve   h+4t-8  = 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  h+4t-8  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when h = 0 the value of t is 2/1 so this line "cuts" the t axis at t= 2.00000

  t-intercept = 8/4  =  2 

Calculate the X-Intercept :

When t = 0 the value of h is 8/1 Our line therefore "cuts" the h axis at h= 8.00000

  h-intercept = 8/1  =  8.00000 

Calculate the Slope :

Slope is defined as the change in t divided by the change in h. We note that for h=0, the value of t is 2.000 and for h=2.000, the value of t is 1.500. So, for a change of 2.000 in h (The change in h is sometimes referred to as "RUN") we get a change of 1.500 - 2.000 = -0.500 in t. (The change in t is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     = -0.500/2.000 = -0.250 

Geometric figure: Straight Line

1.   Slope = -0.500/2.000 = -0.250
2.   h-intercept = 8/1 = 8.00000
3.   t-intercept = 8/4 = 2