Question

The equation of a line in point-slope form is given below:

y + 4 = 2(x + 1)

What is the equation of this line written in Standard Form?


A. -2x + y = -2


B. 2x - y = -2


C. -2x - y = -2


D. 2x + y = 2

Answer 1

We must translate the equation from y-y1=m(x-x1) to ax+by=c from.

Distribute the 2 into x and 1

y+4=2x+2

Combine like terms and move terms:

-2x+y=-4+2

Simplify:

-2x+y=-2

-2x+y=-2 is in standard form

Answer 2

Answer:

$\textsf{A.} \quad -2x + y = -2$

Step-by-step explanation:

$\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\ Ax+By=C \\\\where:\\ \phantom{ww} \bullet A, B and C are constants. \\ \phantom{ww} \bullet A must be positive.\\\end{minipage}}$

Given equation:

$y + 4 = 2(x + 1)$

Distribute the right side of the equation:

$\implies y+4=2x+2$

Subtract 2 from both sides:

$\implies y+4-2=2x+2-2$

$\implies y+2=2x$

Subtract y from both sides:

$\implies y+2-y=2x-y$

$\implies 2=2x-y$

Switch sides:

$\implies 2x-y=2$

Therefore, the equation of the line written in standard form is:

$\boxed{2x-y=2}$

Since this is not one of the answer options, switch the signs:

$\implies -2x+y=-2$

Please note that this is not in standard form, since the coefficient of the term in x is negative.  However, as the equation in strict standard form is not a given answer option, the only answer can be -2 + y = -2.