SOLUTION: the straight line which passes through the points A(1,2) and B(3,a) is perpendicular to the line, y-2x+8=0. calculate the value of "a" How do I work this out? Please help.

Algebra ->  Number-Line -> SOLUTION: the straight line which passes through the points A(1,2) and B(3,a) is perpendicular to the line, y-2x+8=0. calculate the value of "a" How do I work this out? Please help.       Log On


   

Question 893584: the straight line which passes through the points A(1,2) and B(3,a) is perpendicular to the line,
y-2x+8=0. calculate the value of "a"
How do I work this out? Please help.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
y-2x%2B8=0 the given line.
y=2x-8, given line in slope-intercept form.
Slope is 2.

The slope for a line perpendicular to the given line will be highlight_green%28-%281%2F2%29%29.
The slopes of two perpendicular lines will be negative reciprocals.
2%28-1%2F2%29=-1

Formula for slope using the two points of the line perpendicular to the given line:
m=%28a-2%29%2F%283-1%29
-%281%2F2%29=%28a-2%29%2F%283-1%29
-%281%2F2%29=%28a-2%29%2F2
-1=a-2
a=-1%2B2
highlight%28a=3%2F2%29