document.write( "Question 1155051: What is the slope of a line perpendicular to the line whose equation is 12x-9y=135 fully reduce your answer \n" ); document.write( "
Algebra.Com's Answer #777602 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
the equation is in standard form of ax + by = c
\n" ); document.write( "the equation is 12x - 9y = 135
\n" ); document.write( "convert to slope intercept form as follows:
\n" ); document.write( "add 9y to both sides of the equation and subtract 135 from both sides of the equation to get 12x - 135 = 9y
\n" ); document.write( "this is the same as 9y = 12x - 135
\n" ); document.write( "divide both sides of the equation by 9 to get:
\n" ); document.write( "y = 12/9 * x - 135 / 9
\n" ); document.write( "simplify to get y = 4/3 * x - 15
\n" ); document.write( "that's your regular equation.
\n" ); document.write( "the line perpendicular to it will have a slope that is a negative reciprocal of the slope of the regular equaton.
\n" ); document.write( "that makes the slope equal to -3/4
\n" ); document.write( "the general form of a slope intercept equation is y = mx + b
\n" ); document.write( "m is the slope
\n" ); document.write( "b is the y-intercept
\n" ); document.write( "when m = -3/4, the equation becomes y = -3/4 * x + b
\n" ); document.write( "b can be any value.
\n" ); document.write( "for example, when b = 0, the equation of the line perpendicular to the regular line is y = -3/4.
\n" ); document.write( "the standard form of the perpendicular line is calculated as shown below.
\n" ); document.write( "start with y = -3/4 * x
\n" ); document.write( "add -3/4 * x to both sides of the equation to get:
\n" ); document.write( "y + 3/4 * x = 0
\n" ); document.write( "rearrange the terms so the x term is ahead of they term to get:
\n" ); document.write( "3/4 * x + y = 0
\n" ); document.write( "multiply both sides of the equation by 4 to get:
\n" ); document.write( "3x + 4y = 0
\n" ); document.write( "that's the standard form of the equation.
\n" ); document.write( "the equations can be graphed.
\n" ); document.write( "the graph looks like this.
\n" ); document.write( "\"$$$\"
\n" ); document.write( "the first two equations are equivalent to each other, and the second two equations are equivalent to each other.
\n" ); document.write( "each pair is the standard form of the equation and the slope intercept form of the same equation.
\n" ); document.write( "you can see that those two forms of each equation draw the same line.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );