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You can put this solution on YOUR website!
the line is perpendicular to is:
\n" ); document.write( "-4x + 3y = 13
\n" ); document.write( "you have to put this equation into slope intercept form.
\n" ); document.write( "add 4x to both sides of this equation to get:
\n" ); document.write( "3y = 4x + 13
\n" ); document.write( "divide both sides of this equation by 3 to get:
\n" ); document.write( "y = (4/3)x + (13/3)
\n" ); document.write( "that gets you the equation of the line that you have to be perpendicular to into slope intercept form.
\n" ); document.write( "the general of slope intercept form is:
\n" ); document.write( "y = mx + b
\n" ); document.write( "m equals the slope.
\n" ); document.write( "b equals the y intercept.
\n" ); document.write( "the slope of the line formed by this equation is (4/3)
\n" ); document.write( "for a line to be perpendicular to it, the slope of that line has to be the negative reciprocal of it.
\n" ); document.write( "the negative reciprocal of (4/3) is equal to -(3/4).
\n" ); document.write( "that the slope of your new line.
\n" ); document.write( "the general form of your new line becomes:
\n" ); document.write( "y = -(3/4)x + b
\n" ); document.write( "your new line goes through the point (-7,5)
\n" ); document.write( "replace x with -7 and y with 5 in the slope intercept form of your new line to get:
\n" ); document.write( "5 = -(3/4)(-7) + b
\n" ); document.write( "solve for b.
\n" ); document.write( "simplify the equation to get:
\n" ); document.write( "5 = (21/4) + b
\n" ); document.write( "subtract (21/4) from both sides of this equation to get:
\n" ); document.write( "5 - (21/4) = b
\n" ); document.write( "simplify to get:
\n" ); document.write( "-1/4 = b
\n" ); document.write( "that's your answer in fraction form.
\n" ); document.write( "the equation of the line perpendicular to your original line and passing through the point (-7,5) is:
\n" ); document.write( "y = -(3/4)x - (1/4)
\n" ); document.write( "let's see if that's true.
\n" ); document.write( "the graph of your 2 lines is shown below:
\n" ); document.write( "
\n" ); document.write( "they look perpendicular to each other.
\n" ); document.write( "their y intercepts should be:
\n" ); document.write( "original equation y intercept = (13/3)
\n" ); document.write( "perpendicular equation y intercept = -(1/4)
\n" ); document.write( "i placed horizontal lines as y = (13/3) and -(1/4) to see if the y intercepts are correct.
\n" ); document.write( "that graph looks like this:
\n" ); document.write( "
\n" ); document.write( "all that's required to see if if the perpendicular line passes through the point (-7,5).
\n" ); document.write( "i placed a vertical line at x = -7 and a horizontal line at y = 5 to see if that point is on the perpendicular line.
\n" ); document.write( "that graph is shown below:
\n" ); document.write( "
\n" ); document.write( "since the line of the perpendicular equation intersects with the lines x = -7 and y = 5, this means that the point (-7,5) is on the line of the perpendicular equation.
\n" ); document.write( "everything check out, so the equation of the line perpendicular to the original line is:
\n" ); document.write( "y = -(3/4)x - (1/4)
\n" ); document.write( " \n" ); document.write( "