Question

If the line passing through the points
(a, 1) and (8, 7)
is parallel to the line passing through the points
(4, 9) and (a + 2, 1),
what is the value of a?

Answer 1

If the line is passing through (a,1) and (8, 7). Let its slope be m1
we know that a line passing through two points (x1, y1) and (x2, y2) is given as
\[m=\frac{y2-y1}{x2-x1}\]
now here the two points for first line are (a,1) and (8, 7)
its slope
\[m1=\frac{7-1}{8-a}\]
now slope of second line m2 passing through (4,9) and (a+2, 1)
is given as
\[m2=\frac{1-9}{a+2-4}\]
we know parallel lines have same slope
so
\[m1=m2\]
\[\frac{7-1}{8-a}=\frac{1-9}{a+2-4}\]
now we have
\[\frac{6}{8-a}=\frac{-8}{a-2}\]
cross multiplying we get
\[6a-12=-64+8a\]
bringing like terms on same side
we get
\[-2a=-52\]
we get a
\[a=26\]

Answer 2

bless youu!