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3 years ago

How do I solve 2+1/6y=3x+4 for y

Mathematics

1 answer:

oksano4ka [1.4K]3 years ago

6 0

Answer:

Step-by-step explanation:Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

2+(1)/(6)*y-(3*x+4)=0

STEP

Simplify —

Equation at the end of step

(2 + (— • y)) - (3x + 4) = 0

STEP

Rewriting the whole as an Equivalent Fraction

2.1 Adding a fraction to a whole

Rewrite the whole as a fraction using 6 as the denominator :

2 2 • 6

2 = — = —————

1 6

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

2 • 6 + y y + 12

————————— = ——————

6 6

Equation at the end of step

(y + 12)

———————— - (3x + 4) = 0

STEP

Rewriting the whole as an Equivalent Fraction

3.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 6 as the denominator :

3x + 4 (3x + 4) • 6

3x + 4 = —————— = ————————————

1 6

Adding fractions that have a common denominator :

3.2 Adding up the two equivalent fractions

(y+12) - ((3x+4) • 6) y - 18x - 12

————————————————————— = ————————————

6 6

Equation at the end of step

y - 18x - 12

———————————— = 0

STEP

When a fraction equals zero

4.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

y-18x-12

———————— • 6 = 0 • 6

Now, on the left hand side, the 6 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

y-18x-12 = 0

Equation of a Straight Line

4.2 Solve y-18x-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 y-18x-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 12/1 so this line "cuts" the y axis at y=12.00000

y-intercept = 12/1 = 12.00000

Calculate the X-Intercept :

When y = 0 the value of x is 2/-3 Our line therefore "cuts" the x axis at x=-0.66667

x-intercept = 12/-18 = 2/-3 = -0.66667

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 12.000 and for x=2.000, the value of y is 48.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 48.000 - 12.000 = 36.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = 36.000/2.000 = 18.000

Geometric figure: Straight Line

Slope = 36.000/2.000 = 18.000

x-intercept = 12/-18 = 2/-3 = -0.66667

y-intercept = 12/1 = 12.00000

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