SOLUTION: Find an equation of the line that passes through the point (-1,3) and is parallel to the line passing through the points (-2,-3) and (2,5).

Algebra ->  Linear-equations -> SOLUTION: Find an equation of the line that passes through the point (-1,3) and is parallel to the line passing through the points (-2,-3) and (2,5).      Log On


   

Question 319019: Find an equation of the line that passes through the point (-1,3) and is parallel to the line passing through the points (-2,-3) and (2,5).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First find the line.
The formula for the slope of a line is,
m=%28y2-y1%29%2F%28x2-x1%29=%285-%28-3%29%29%2F%282-%28-2%29%29=8%2F4=2
Parallel lines have identical slopes.
m1=m2=2
y=2x%2Bb
Use the point (-1,3) to solve for b.
3=-2%2Bb
b=5
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Parallel Line
highlight%28y=2x%2B5%29
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I inadvertently solved for the perpendicular line first and then realized that you were looking for a parallel line.
Here's how to do it if you're looking for a line perpendicular to your original line that goes through (-1,3).
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Perpendicular lines have slopes that are negative reciprocals,
m1%2Am2=-1
2%2Am2=-1
m2=-1%2F2
The slope of the second line is m=-1%2F2
y=-%281%2F2%29x%2Bb
Use the point (-1,3) to solve for b.
3=-%281%2F2%29%28-1%29%2Bb
b=3-1%2F2
b=5%2F2
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Perpendicular Line
highlight_green%28y=-%281%2F2%29x%2B5%2F2%29
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