Answer:
Explanation:
Equation at the end of step 1
(12 • (m + 3x)) - 18 • (x - 3) = 0
Equation at the end of step 2
12 • (m + 3x) - 18 • (x - 3) = 0
Pulling out like terms
4.1 Pull out like factors :
12m + 18x + 54 = 6 • (2m + 3x + 9)
Equation at the end of step
4
:
6 • (2m + 3x + 9) = 0
STEP
5
:
Equations which are never true:
5.1 Solve : 6 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
5.2 Solve 2m+3x+9 = 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 2m+3x+9 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of m is -9/2 so this line "cuts" the m axis at m=-4.50000
m-intercept = -9/2 = -4.50000
Calculate the X-Intercept :
When m = 0 the value of x is -3/1 Our line therefore "cuts" the x axis at x=-3.00000
x-intercept = -9/3 = -3
Calculate the Slope :
Slope is defined as the change in m divided by the change in x. We note that for x=0, the value of m is -4.500 and for x=2.000, the value of m is -7.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -7.500 - (-4.500) = -3.000 in m. (The change in m is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -3.000/2.000 = -1.500
Geometric figure: Straight Line
Slope = -3.000/2.000 = -1.500
x-intercept = -9/3 = -3
m-intercept = -9/2 = -4.50000