Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4*a+b-(12)=0
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 4a+b-12 = 0 and calculate its properties
Notice that when a = 0 the value of b is 12/1 so this line "cuts" the b axis at b=12.00000
b-intercept = 12/1 = 12.00000
When b = 0 the value of a is 3/1 Our line therefore "cuts" the a axis at a= 3.00000
a-intercept = 12/4 = 3
Slope is defined as the change in b divided by the change in a. We note that for a=0, the value of b is 12.000 and for a=2.000, the value of b is 4.000. So, for a change of 2.000 in a (The change in a is sometimes referred to as "RUN") we get a change of 4.000 - 12.000 = -8.000 in b. (The change in b is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -8.000/2.000 = -4.000
Geometric figure: Straight Line
- Slope = -8.000/2.000 = -4.000
- a-intercept = 12/4 = 3
- b-intercept = 12/1 = 12.00000
