document.write( "Question 733928: How can I solve this? I don't understand at all... \"Write an equation for a line perpendicular to y=-3x+4\" \n" ); document.write( "

Algebra.Com's Answer #448675 by KMST(5328) $\"\"$ $\"About$

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The slopes of perpendicular lines multiply to yield $\"%28-1%29\"$ .
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\n" ); document.write( "The equation $\"y=-3x%2B4\"$ represents a line that crosses they-axis at $\"y=4\"$ because when $\"x=0\"$ --> $\"y=4\"$ .
\n" ); document.write( "The line has $\"slope=-3\"$ , meaning that as x increases by 1, y \"increases\" by -3 (meaning that it decreases by 3).
\n" ); document.write( "The line looks like this:
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The blue-and-red triangle shows how an increase of 1 in x means an \"increase\" of -1 in y.
\n" ); document.write( "We can draw many perpendicular lines. I will draw a perpendicular line that goes through (0,4) like this
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The green-and-red triangle is the blue and-red triangle rotated $\"90%5Eo\"$ .
\n" ); document.write( "Its sides are perpendicular to the corresponding sides of the blue-and-red triangle.
\n" ); document.write( "That makes the blue and green lines perpendicular to each other.
\n" ); document.write( "The green-and-red triangle shows that for the green line, an increase of 3 in x translates into an increase of 1 in y, meaning that the slope of the green line is $\"1%2F3\"$ .
\n" ); document.write( "The equation of the green line is $\"y=%281%2F3%29x%2B4\"$ .
\n" ); document.write( "The slopes of perpendicular lines multiply to yield $\"%28-1%29\"$ because in those rotated right triangles the ratio of vertical leg to horizontal leg is reversed (the ratios are reciprocals), but if one of the (change in y)/(change inx) ratios in positive, the other must be negative, so the product will be not 1, but -1. \n" ); document.write( "

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