Question 243718: how do i find out if a graph on an equation will be parallel or perpendicular if only given the points?
EX. (3,1) (5,3) is the graph of the equation parallel, perpendicular or neither?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! 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:
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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:
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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:
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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:
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