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tghe x-intercept is -3/7
\n" ); document.write( "the line is perpendicular to the line defined by the equation 3x + 4y = 10
\n" ); document.write( "convert that equation to slope intercept form as shown below:
\n" ); document.write( "start with 3x + 4y = 10
\n" ); document.write( "subtract 3x from both sides of the equation to get:
\n" ); document.write( "4y = 10 - 3x
\n" ); document.write( "divide both sides of the equation by 4 to and reorder the terms in descending order of degree to get:
\n" ); document.write( "y = -3/4 * x + 10/4.
\n" ); document.write( "that line is now in the slope intercept form of y = mx + b.
\n" ); document.write( "m is the slope and b is the y-intercept.
\n" ); document.write( "the line perpendicular to this line will have a slope that is a negative reciprocal to it.
\n" ); document.write( "that makes the slope of the perpendicular line equal to 4/3.
\n" ); document.write( "the slope intercept form of the equation of that perpendicular line is y = 4/3 * x + b
\n" ); document.write( "b is the y-intercept of the line.
\n" ); document.write( "if the x-intercept of that line is -3/7, then a point on that line is (-3/7,0).
\n" ); document.write( "to find the value of b, replace x with -3/7 and y with 0 to get:
\n" ); document.write( "y = 4/3 * x + b becomes 0 = 4/3 * -3/7 + b
\n" ); document.write( "4/3 * -3/7 is equal to -12/21.
\n" ); document.write( "the equation becomes 0 = -12/21 + b
\n" ); document.write( "solve for b to get b = 12/21.
\n" ); document.write( "the equation of the line perpendicular to the original line is y = 4/3 * x + 12/21.
\n" ); document.write( "here's a graph of both lines.\r
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\n" ); document.write( "\n" ); document.write( "the red line is the original line.
\n" ); document.write( "you can see that it intersects with the y-axis at the point (0,2.5)
\n" ); document.write( "that means it's y-intercept is 2.5 which is the same as 10/4.
\n" ); document.write( "the blue line is the line that's perpendicular to it.
\n" ); document.write( "you can see that the x-intercept of that line is at the point (-.429,0).
\n" ); document.write( "-.429 is the decimal form of -3/7 rounded to 3 decimal places.
\n" ); document.write( "the y-intercept is the value of x when y = 0.
\n" ); document.write( "the x-intercept is the value of y when x = 0.\r
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