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3 years ago

what is the equation of a line parallel to the line 2x-3y=6 and that passes through the point (-6,12)

Mathematics

1 answer:

Brrunno [24]3 years ago

8 0

Hello from MrBillDoesMath!

Answer:

y = (2/3)x + 16

Discussion:

Given line:

2x - 3y = 6 => add 3y to both sides

2x = 6 + 3y => subtract 6 from both sides

2x -6 = 3y => divide both sides by 3

y =(2/3)x - 2

The slope of this line, m, (2/3) and any line parallel to the given line has the same slope. We are looking for the line with slope (2/3) passing through (-6, 12)

y = (2/3)x + b => substitute (x,y) = (-6, 12) in the equation

12 = (2/3)(-6) + b => add (2/3)(6) = 12/3 = 4

12 + 4 = (2/3)(-6) + (2/3)(6) + b => as (2/3)(-6) + (2/3)(6) = 0

12 +4 = 0 + b =>

b = 16

Hence the equation of the parallel line through ( -6,12) is

y = mx + b

=(2/3)x + 16

Check: is (-6,12) on this line? Does 12 = (2/3)(-6) + 16 = -4 + 16 = 12? Yes!

Thank you,

MrB

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