SOLUTION: Write an equation of the line in standard form with integer coefficients. the line through (8, 3) perpendicular to x + 2y = 6

Algebra ->  Linear-equations -> SOLUTION: Write an equation of the line in standard form with integer coefficients. the line through (8, 3) perpendicular to x + 2y = 6      Log On


   

Question 664512: Write an equation of the line in standard form with integer coefficients.
the line through (8, 3) perpendicular to x + 2y = 6
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
A perpendicular line has a negative reciprocal slope.
...
Starting with x+2y=6, convert it into the linear equation format
x+2y=6
2y = -x+6
y = -1%2F2x + 6%2F2 which is the same as y = -1%2F2x + 3
...
The slope of the lines is -1%2F2.
A perpendicular line will have a slope of %28-1%29%2F%28-1%2F2%29
Where dividing is the same as multiplying the inverse,
%28-1%29%2F%28-1%2F2%29 is the same as -1%2A%28-2%2F1%29 = 2
.
More easily, the negative inverse of -1%2F2%29 is %282%2F1%29+=+2
...
Knowing the slope of 2 and using the coordinates (8, 3), solve for y-intercept, b.
3 = 2(8) + b
b = 3 - 16 = -13
...
The equation of the perpendicular line that passes through (8, 3) is
y = 2x - 13 :slope-intercept from
2x - y - 13 = 0 :standard form
.....
Red line: y = -1%2F2x + 3
Green line: y = 2x - 13
graph%28300%2C200%2C-2%2C10%2C-20%2C10%2C+%28-1%2F2%29x%2B3%2C+2x-13%29
....................
Delighted to help.
-Reading Boosters
Wanting for others what we want for ourselves.
www.MyHomeworkAnswers.com