Answer:
Step by Step Solution
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Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
9*x-12*y-(36)=0
STEP
1
:
Pulling out like terms :
1.1 Pull out like factors :
9x - 12y - 36 = 3 • (3x - 4y - 12)
Equation at the end of step
1
:
STEP
2
:
Equations which are never true :
2.1 Solve : 3 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
2.2 Solve 3x-4y-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 3x-4y-12 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 3/-1 so this line "cuts" the y axis at y=-3.00000
y-intercept = 12/-4 = 3/-1 = -3.00000
Calculate the X-Intercept :
When y = 0 the value of x is 4/1 Our line therefore "cuts" the x axis at x= 4.00000
x-intercept = 12/3 = 4
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -3.000 and for x=2.000, the value of y is -1.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -1.500 - (-3.000) = 1.500 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 1.500/2.000 = 0.750
Geometric figure: Straight Line
Slope = 1.500/2.000 = 0.750
x-intercept = 12/3 = 4
y-intercept = 12/-4 = 3/-1 = -3.00000
