Question 243718
Given the two points, you can draw a line.  But any line will be perpendicular to any other line that has a slope = negative inverse of the first line; and it will be parallel to any line that has the same slope.  So you need to give us more information in your problem statement.
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With two points, you can determine the slope = change in y divided by change in x, which is also known as the rise over the run.
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(x1,y1) = (3,1)
(x2,y2) = (6,3)
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m = slope = (y2 - y1) / (x2 - x1)
m = (3-1) / (6-3)
m = 2/3
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The slope-intercept formula for a line is:  y = mx + b.
We only have a value for m, so we cannot determine the y-intercept (that is, where it crosses the y-axis when x=0).
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We can 'assume' b = 0 to be able to draw a line to show you what the line looks like.
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y = 2/3x + 0.
Graph:
{{{
graph(500,500,-10,10,-10,10, 2/3*x)
}}}
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As I mentioned above, a line with negative inverse slope will be perpendicular. 
Given y = 2/3x, then the perpendicular line will be y = -3/2x.
Graph:
{{{
graph(500,500,-10,10,-10,10, 2/3*x, -3/2*x)
}}}
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A parallel line will have the same slope, but a different y-intercept. So, we'll 'assume' the second intercept is 3 so that the graph will show the parallel.
y = 2/3x + 3
Graph:
{{{
graph(500,500,-10,10,-10,10, 2/3*x, 2/3*x+3,-3/2*x)
}}}
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To finish this lesson, we can plot a line parallel to the first perpendicular.  Let's assume a y-intercept of -4, so y = -3/2x - 4.
Graph:
{{{
graph(500,500,-10,10,-10,10, 2/3*x, 2/3*x+3,-3/2*x, -3/2*x-4)
}}}