Please help

Question

If the line passing through the points (a,2) and (6,7) is parallel to the passing through the points (4,8) and (a+3,2) what is the value of a?

Answer 1

parallel lines have the same slope

slope of the first line...

(a,2), (6,7)

(7-2)/(6-a)=5/(6-a)

slope of the second line...

(4,8), (a+3,2)

(8-2)/(4-[a+3])=6/(4-a-3)=6/1-a)

sets the slopes equal to each other

5/(6-a)=6/(1-a)

cross multiply

5(1-a)=6(6-a)

5-5a=36-6a

6a-5a=36-5

a=31

check: (31,2), (6,7), slope=5/-25=-1/5

          (4,8), (34,2), slope=6/-30=-1/5

Answer 2

Parallel means they must have the same slope.  Slope is rise/run, so set the two equal to each other and solve for a.

 

 Slope of first line:

(7-2)/(6-a) = 5/(6-a)

Slope of second line:

(2-8)/((a+3)-4) = -6/(a-1)

 

5/(6-a) = -6/(a-1)

5a-5 = -36 +6a

-a = -31

a = 31