Question

How do you get this to its Standard Form?And is it linear?

Answer 1

x/2 = (y+3) /6

using cross products

6* x = 2 * (y+3)

distribute

6x = 2y+6

subtract  2y from each side

6x -2y = 6

we can simplify this by dividing each term by 2

3x - y = 3

this is the standard form of a line (Ax + By =C)

this is linear because x and y are only to the first power)

Answer 2

let's bear in mind that

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

so, let's do away with the denominators by multiplying both sides by the LCD of all fractions, in this case 6.

$\bf \cfrac{x}{2}=\cfrac{y+3}{6}\implies\stackrel{\textit{multiplying by }\stackrel{LCD}{6}}{6\left( \cfrac{x}{2} \right)=6\left( \cfrac{y+3}{6} \right)}\implies 3x=y+3\implies \stackrel{\textit{standard form}}{3x-y=3}$