SOLUTION: perpendicular to 3x-2y=-1; through (2,-7) find an equation of each line function notation satisfying the conditions given.

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Question 106451This question is from textbook intermediate algebra
: perpendicular to 3x-2y=-1; through (2,-7)
find an equation of each line function notation satisfying the conditions given. This question is from textbook intermediate algebra

Answer by solver91311(24713) About Me  (Show Source):
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In order to find a perpendicular line, you first need to find the slope of the original line and then find the negative reciprocal.

3x-2y=-1

needs to be put into y+=+mx%2Bb form.

-2y=-3x-1
y=3x%2F2%2B1

Hence, the slope of the line is 3%2F2 and the slope of any perpendicular line would be -2%2F3

also, since y is a function of x in this case, the equation in function notation would be f%28x%29=3x%2F2%2B1

Since you are given a point to further define your perpendicular, you need to use the point-slope form of a line, given by:

y-y1=m%28x-x1%29

Substituting:

y-%28-7%29=%28-2%2F3%29%28x-2%29

And rearranging into slope-intercept form:

y=-2x%2F3-17%2F3

or in function notation,

f%28x%29=-2x%2F3-17%2F3

EXTRA CREDIT: Graph these two lines and verify visually that they are perpendicular.