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

Answers

  1. 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.

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  2. 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

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