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


   

Question 664514: Write an equation of the line in standard form with integer coefficients.

the line through (8, 3) parallel to x + 2y = 6
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Parallel lines have the same slope.
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First, structure the given line in the y = mx+b format
x + 2y = 6
Isolate y
2y = 6 - x, which is the same as 2y = -x + 6
Divide both sides by 2
y = -1%2F2x + 6%2F2 or y = -1%2F2x + 3
...
Slope of this line is -1%2F2
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For the parallel line, we now know the slope, m, is -1%2F2 and
using the coordinates (8,3), solve for y-intercept, b.
3 = %28-1%2F2%29%288%29 + b
3 = -4 + b
b = 3 + 4 = 7
...
The parallel line passing through (8,3) is
y = -1%2F2x + 7 : slope-intercept form
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To find Standard Form
1%2F2x + y = 7
Multiply entire equation by 2 to remove fraction
%281%2Fcross%282%29%29%28cross%282%29%29x + 2y = 7(2)
x + 2y - 14 = 0 : standard form
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Red line: y = -1%2F2x + 3
Green line: y = -1%2F2x + 7
graph%28300%2C200%2C-5%2C20%2C-10%2C10%2C%28-1%2F2%29x%2B3%2C+%28-1%2F2%29x%2B7%29
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-Reading Boosters
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