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Write an equation in standard form for the line that passes through the given points

(5, -3) and (5,6)

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Answer:


x=5

Explanation:

The standard form for equation of the line is
Ax + By = C \\

We first find the slope of the line:

Slope, m is given by:


{\displaystyle {\Delta y\over \Delta x}={y_1-y_2\over x_1-x_2}}


{\displaystyle m={-3-6\over 5-5}={-8\over 0}=\infty}

This means that the slope is undefined.

And that the line is perpendicular to the x-axis and parallel to the y -axis.

Being that the line is parallel to the y-axis it means that the line intersect at no point with the y-axis so our equation is solved as follows:

Pick any point
(x,y)along the line and one of the known points, say,
(5,6)

So in solving for m,

we find that :


{\displaystyle {y_1-y_2\over x_1-x_2}={y-6\over x-5}={-8\over 0}}

Cross multiplication gives us:


0(y-6)=-8(x-5)


-8(x-5)=0

Dividing through by
-8 , we get:


x-5=0


x=5

User Bobbi
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