Question

Which equation represents the line that passes through the points (2,7) and (1,5)

Answer 1

Answer:

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)

Step-by-step explanation: