Write an equation in standard form for a line perpendicular to x+3y=6 and passing through (-3,5)

tophergopher3wo

tophergopher3wo

Answered question

2022-09-11

Write an equation in standard form for a line perpendicular to x+3y=6 and passing through (-3,5)

Answer & Explanation

acilschoincg8

acilschoincg8

Beginner2022-09-12Added 12 answers

Given an equation in x and y of a line, then you can construct the equation of a perpendicular line by swapping x and y and reversing the sign of one of them.
This is equivalent to reflecting the original line in the 45 o line with equation y=x then reflecting in one of the axes.
So in your example, we can replace the original
x+3y=6
with
y−3x=6
to get a perpendicular line.
Then adding 3x to both sides we get:
y=3x+6
which is in standard slope intercept form, with slope 3 and intercept 6
The line we want to construct is parallel to this, so will have the same slope, 3, but probably a different intercept.
Given the slope 3 and the point (−3,5), we can write the equation of the desiblack line in standard point slope form as:
y - 5 = 3 ( x - ( - 3 ) ) = 3 ( x + 3 )
To convert this to slope intercept form, add 5 to both sides to get:
y = 3 ( x + 3 ) + 5 = 3 x + 9 + 5 = 3 x + 14

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