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lyudmila [28]
3 years ago
11

How to I make 3x+6y=18 into y=my+b

Mathematics
1 answer:
kirza4 [7]3 years ago
3 0

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


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