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

Question

Mathematics

Amirah Oconnell

14 August, 19:29

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

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Answers (1)

Know the Answer?

Raul Snyder · Answer 1

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