Question

Given the equation y − 3 = one half(x + 6) in point-slope form, identify the equation of the same line in standard form.

a- x − 2y = −12
b- y = one halfx
c- y = one halfx + 6
d-y = one halfx + 9

Answer 1

bearing 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

`\bf y-3=\cfrac{1}{2}(x+6)\implies y-3=\cfrac{1}{2}x+3\implies y=\cfrac{1}{2}x+6 \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2(y)=2\left( \cfrac{1}{2}x+6 \right)}\implies 2y=x+12\implies -x+2y=12 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill x-2y=-12~\hfill`

Answer 2

a

Explanation:

Given

y - 3 =
`(1)/(2)`(x + 6)

Multiply through by 2 to clear the fraction

2y - 6 = x + 6 ( subtract 2y from both sides )

- 6 = x - 2y + 6 ( subtract 6 from both sides )

- 12 = x - 2y, that is

x - 2y = - 12 → a