SOLUTION: Problem #1 Line l goes through (1,3) and is parallel to the line through (4,3) and (-3,1). Find the slope of l. Thanks for your help on this one. I am really lost.

Algebra ->  Linear-equations -> SOLUTION: Problem #1 Line l goes through (1,3) and is parallel to the line through (4,3) and (-3,1). Find the slope of l. Thanks for your help on this one. I am really lost.      Log On


   

Question 105681: Problem #1
Line l goes through (1,3) and is parallel to the line through (4,3) and (-3,1). Find the slope of l.



Thanks for your help on this one. I am really lost.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Line l goes through (1,3).
Line 1 is parallel to the line through (4,3) and (-3,1)
Let's call that line 2.
First, let's find the slope of line 2.
Then, we'll find the equation for line 1.
The slope of a line through two points is given by the formula:
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
In your case,
m%5B2%5D=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m%5B2%5D=%281-3%29%2F%28-3-4%29
m%5B2%5D=%28-2%29%2F%28-7%29
m%5B2%5D=2%2F7
Parallel lines have the same slope.
m%5B1%5D=m%5B2%5D=2%2F7
The slope-intercept form of the line is
y=mx%2Bb
Since line 1 goes through (1,3), we can use that information to solve.
y=mx%2Bb
3=2%2F7%2A%281%29%2Bb
b=3-2%2F7
b=21%2F7-2%2F7
b=19%2F7
y=%282%2F7%29x%2B19%2F7
Here's how it all looks graphically.