Solution - Properties of a straight line
Step by Step Solution
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
8*v+8*b-(240)=0
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
8v + 8b - 240 = 8 • (v + b - 30)
Equation at the end of step 1 :
Step 2 :
Equations which are never true :
2.1 Solve : 8 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
2.2 Solve v+b-30 = 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 v+b-30 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when v = 0 the value of b is 30/1 so this line "cuts" the b axis at b=30.00000
b-intercept = 30/1 = 30.00000 Calculate the X-Intercept :
When b = 0 the value of v is 30/1 Our line therefore "cuts" the v axis at v=30.00000
v-intercept = 30/1 = 30.00000 Calculate the Slope :
Slope is defined as the change in b divided by the change in v. We note that for v=0, the value of b is 30.000 and for v=2.000, the value of b is 28.000. So, for a change of 2.000 in v (The change in v is sometimes referred to as "RUN") we get a change of 28.000 - 30.000 = -2.000 in b. (The change in b is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -2.000/2.000 = -1.000 Geometric figure: Straight Line
- Slope = -2.000/2.000 = -1.000
- v-intercept = 30/1 = 30.00000
- b-intercept = 30/1 = 30.00000
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