# SOLUTION: Write the equation of each line. Give the answer in standard formusing only integers as the coefficients. The line through (2,-3) that is perpendicular to the line y=-3x+12 The

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Question 118012: Write the equation of each line. Give the answer in standard formusing only integers as the coefficients.
The line through (2,-3) that is perpendicular to the line y=-3x+12
How do I work the problem to find the answer given?

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 Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of , you can find the perpendicular slope by this formula: where is the perpendicular slope So plug in the given slope to find the perpendicular slope When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second Multiply the fractions. So the perpendicular slope is So now we know the slope of the unknown line is (its the negative reciprocal of from the line ). Also since the unknown line goes through (2,-3), we can find the equation by plugging in this info into the point-slope formula Point-Slope Formula: where m is the slope and (,) is the given point Plug in , , and Distribute Multiply Subtract from both sides to isolate y Make into equivalent fractions with equal denominators Combine the fractions Reduce any fractions So the equation of the line that is perpendicular to and goes through (,) is So here are the graphs of the equations and graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)

Now let's convert to standard form

 Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa) Start with the given equation Subtract from both sides Rearrange Multiply both sides by 3 Distribute Multiply Reduce Reduce2 Now the equation is in standard form where , , and

Since the answer is , I'm assuming that the book wants A to be positive.

Multiply both sides of by -1

Distribute and multiply