SOLUTION: Find the equation of the line that contains point (12,-7) and perpendicular to the line whose equation is 4y-3x+9=0

Question 251333: Find the equation of the line that contains point (12,-7) and perpendicular to the line whose equation is 4y-3x+9=0
Found 2 solutions by richwmiller, solver91311:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
first find m for 4y-3x+9=0
4y=3x-9
y=3x/4+9/4
m=3/4
perpendicular m=-4/3
y=mx+b
y=-4/3x+b
-7=-4/3(12)x+b
-7=-4*4+b
9=b
y=-4/3x+9

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Sorry, this question cannot be answered exactly as you posed it. For any given line, there are an infinite number of equations which solution sets are the ordered pairs that comprise the line. While most are only trivially different, the fact that you can put any two variable linear equation into several forms means there is more than one representation non-trivially different. Hence, finding "the" equation of a line is impossible. Below a method to find "an" equation of the desired line.

Step 1. Solve the given equation for y in terms of everything else, that is, put it into slope intercept form,

Step 2. Determine the slope of the line represented by the given equation by inspection of the coefficient on .

Step 3. Calculate the slope of any line perpendicular to the given line by determining the negative reciprocal of the slope determined in 2 -- because:

Step 4. Use the point-slope form of an equation of a line along with the given point and the slope determined in step 3 to write a form of the desired equation.

where is the given point and is the slope determined in step 3.

Step 5. If necessary, either because of instructions provided in your text or by your instructor, alter the form of the result of step 4 by normal algebraic means either to the slope-intercept form as discussed in step 1, the standard form, , or whatever form is specified. If no form is specified, then you can certainly consider the problem properly completed if you stop at the end of step 4 -- which is to say that no one can say that the result of step 4, given correctly performed arithmetic and algebraic manipulations, is NOT a representation of the desired line. (Note: some texts require A, B, and C to be integers for proper standard form)

John

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