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Jan 10, 7:17:08 PM Which equation represents a line which is perpendicular to the line x - 2y = -14? Oy= -27 -1 Oy= 2x + 8 Submit Answer Oy=x+4 Oy = -x + 2

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You need to determine which line is perpendicular to the line


x-2y=-14

For two lines to be considered perpendicular their slopes must be the inverse positive, that is, if, for example, you have the lines


y_1=mx_1+b
y_2=nx_2+c

For them to be perpendicular one slope must be the inverse negative of the other such as


n=-(1)/(m)

The first step is to write the given line in slope-intercept form:

1) Pass the x term to the right side of the equal sign


\begin{gathered} x-2y=-14 \\ x-x-2y=-14-x \\ -2y=-x-14 \end{gathered}

2) Divide both sides of the expression by "-2"


\begin{gathered} -(2y)/(-2)=-(x)/(-2)-(14)/(-2) \\ y=(1)/(2)x+7 \end{gathered}

The slope of the line is


m=(1)/(2)

So the slope of a line perpendicular to it will be the inverse negative of it


\begin{gathered} n=-((1)/((1)/(2))) \\ n=-2 \\ \end{gathered}

The correct option is the one that has slope -2

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