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A line passes through (3, -2) and is perpendicular to 3x - 2y = 7.

User Reverb
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6 votes

Answer:

y=-2x/3

Explanation:

Perpendicular lines have opposite reciprocal slopes.

An example of opposite reciprocals: -1/2 and 2

-1*2=-2

The reciprocal of -2 is -1/2.

In order to solve for slope, isolate y:

3x - 2y = 7 ==> solve for y

3x = 7 + 2y ==> add 2y on both sides to make y positive

3x - 7 = 2y ==> isolate y by subtracting 7 on both sides

y = (3x - 7)/2 ==> divide both sides by 2 in order to isolate y

y = 3x/2 - 7/2 ==> distribution

Hence, the slope is 3/2 <== 3x/2.

Now, find the perpendicular slope:

-1*3/2=-3/2

The reciprocal of -3/2 is -2/3 ==> the slope of the perpendicular equation

Now, find the equation of the line that passes through (3, -2):

y=mx+b ==> slope-intercept equation

-2=-2/3 * (3) + b ==> plugin (x=3, y=-2) and m=-2/3 which is the slope.

-2 = 3 * (-2/3) + b ==> solve for b

-2 = -6/3 + b

-2 = -2 + b

b = 0 ==> -2 + 0 = -2

y=-2x/3+0 ==> plugin the slope -2/3 and b=0.

y=-2x/3+0 ==> y=-2x/3

Hence, the equation is y=-2x/3.

User Bautista
by
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