Determine the equation for this line, passing through the y int of the line defined by 2x+3y-18=0 and perpendicular to 4x-9y=27. How would you approach this (we are doing perpendicular and...

Determine the equation for this line, passing through the y int of the line defined by 2x+3y-18=0 and perpendicular to 4x-9y=27.

How would you approach this (we are doing perpendicular and parallel lines)

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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To approach this problem, use the general form of equation of line:

y = mx + b, where m is the slope of line, b is the y intercept 

and use the fact that product of slopes of two perpendicular lines is -1.

Converting the first equation to the standard format, we get:

2x+3y-18 = 0

or y = (-2/3)x + 6

here, y-intercept is 6. so our desired line passes through the point defined by coordinates (0,6).

The second line's equation can similarly be reworked.

4x-9y = 27

or y =(4/9)x - 3

slope of line = 4/9

slope of the desired line = -1/slope of given line  = -1 /(4/9) = -9/4

Now we can find the equation of line with slope (-9/4) and passing through (0,6).

y = mx+b = (-9/4)x+b

This line passes through (0,6), so we can substitute x=0 and y=6 in the equation to get b,

b = 6

thus the equation of line is y= (-9/4) x +6

or simplifying to get

4y+9x=24

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