SOLUTION: Which equation represents the line that passes through (1,1) and is parrallel to the line passing through (2,3) and (1,5)

Algebra ->  Coordinate-system -> SOLUTION: Which equation represents the line that passes through (1,1) and is parrallel to the line passing through (2,3) and (1,5)      Log On


   

Question 166023: Which equation represents the line that passes through (1,1) and is parrallel to the line passing through (2,3) and (1,5)
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

First we get the slope of line with points (2,3) & (1,5):
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%285-3%29%2F%281-2%29=2%2F%28-1%29
m=-2, slope
Knowing the slop, we can get the intercept in point (1,1):
y=mx%2Bb, SLOPE- INTERCEPT
1=-2%281%29%2Bb
b=1%2B2=3
so, the eqn of the line: highlight%28y=-2x%2B3%29
The line with points (2,3) & (1,5): same slope because parallel, we'll check
VIA POINT SLOPE FORM:
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%285-3%29%2F%281-2%29=2%2F-1 ----> m=-2, same right?
For the intercept thru pints (2,3):
Via SLOPE INTERCEPT FORM, we pick points (2,3)
3=-2%282%29%2Bb
b=3%2B4=7 ----> y intercept. The same value if you pick points (1,5).
Eqn of line: y=-2x%2B7 (Green line) parallel to y=-2x%2B3 (Red line)
See the graph,
--- see red line, it passes at point (1,1). Also green line passes points (2,3) & (1,5)
Thank you,
Jojo