SOLUTION: The equation of the line through (3, -1) and parallel to the line through (1,2) and (2,1). Thanks for the big help.. Kindly put the solution..

Algebra ->  Test -> SOLUTION: The equation of the line through (3, -1) and parallel to the line through (1,2) and (2,1). Thanks for the big help.. Kindly put the solution..       Log On


   

Question 187743: The equation of the line through (3, -1) and parallel to the line through (1,2) and (2,1).
Thanks for the big help.. Kindly put the solution..

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


First, we find the Line Eqn thru points (1,2) & (2,1) via Slope-Intercept From;
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29=%281-2%29%2F%282-1%29=-1%2F1=red%28-1%29
Since parallel to the line passing thru (3,-1)---->m%5B1%5D=m%5B2%5D=-1

Then on point (3,-1), via Point Slope-Form:
y=mx%2Bb---->-1=%28-1%29%283%29%2Bb---->b=-1%2B3=2 Y-Intercept

Therefore the Line Eqn-----> y=-x%2B2---> x+y=2 Standard Form
We can get the line eqn to where it is parallel. Thru point (1,2):
y=mx%2Bb---->2=-1%281%29%2Bb---->b=2%2B1=red%283%29
Thru point (2,1): ---->1=%28-1%29%282%29%2Bb --->b=1%2B2=red%283%29
So it follows--->y=-x%2B3
We see the lines:
----> RED, y=-x=3; GREEN, x+y=2, or y=-x%2B2
Thank you,
jojo