Answer:
Step-by-step explanation:
3x+6y=18
Geometric figure: Straight Line
Slope = -1.000/2.000 = -0.500
x-intercept = 6/1 = 6.00000
y-intercept = 6/2 = 3
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3*x+6*y-(18)=0
Step by step solution :
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
3x + 6y - 18 = 3 • (x + 2y - 6)
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 x+2y-6 = 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 x+2y-6 = 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 = 6/2 = 3
Calculate the X-Intercept :
When y = 0 the value of x is 6/1 Our line therefore "cuts" the x axis at x= 6.00000
x-intercept = 6/1 = 6.00000
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 2.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 2.000 - 3.000 = -1.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -1.000/2.000 = -0.500
Geometric figure: Straight Line
Slope = -1.000/2.000 = -0.500
x-intercept = 6/1 = 6.00000
y-intercept = 6/2 = 3
