Maths-
General
Easy
Question
Find the equation for a path that passes through the point (6, 6) and is perpendicular to
.
Hint:
- Perpendicular lines are lines that intersect at a right angle.
The correct answer is: y = 4/3x - 2
- We have been given an equation that represents y-axis.
- We have to find an equation for a path that passes through the point (6, 6) and is perpendicular to
![y equals fraction numerator negative 3 over denominator 4 end fraction x plus 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF8AAAAjCAYAAADyrNZPAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAfdJREFUeNrtms9HBGEYx18rSbpkpUOHWOmUdE2S6JCstSLpkCQ6ddh/IB0S6bA6dOnQIUkkHZJEVpIkkpUkkf6HDmt1qe9jn2WN2V1TM/PMvJ4vH2bfmWF85533+fGuMfHTOLgAJVAG72AbJI0qcF2DadBaMzYELtUaOX2pBTJKgTe1IVx1g0Ve96fUjnD04yCnlvhjpBv11Amy4AGMqZUy6uAXoBJSWS2Q0SAHXVXAugEzoAUkuOL9BAtqTfAaBee8zJS54k1H+Hn7wSoo6qsLXwdguUnWpvKQGvt63x6YdRmn4mXDIuOWwKbL+DqfEzGfgtWWY6ydM4ikz4WRtJ64LVEVtSd2JGc+9UWOHWNrHChs0yTI8/EEKEgvOzS7X2p+d4EP0CbUTvCLerridkTRNN+E8esrb3hdqeY4bxo3q+K87FRj2TcXZ+IBl3RrKn3xFM/6hKXZygg44Qk2FxXz90EGHIJ5S42niXXGyQQ14x6N973fQMzPccr5bKnxFMcuHGanuQgSNz/LF2QsNJ42209Bj8u5I86AgizKmsZDMv0+wgambS7R6ZMcjuiz0fr8aqv5A6bSKYyqdrn81+aUQGpY+GewU/0xUFL21avmhy/qQK74kOapPIpK/zufcmyVR9FfQfrUfBnFuXFn7QtRqflqfqz1C3S+rvlNlaG+AAAAsnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT55PC9taT48bW8+PTwvbW8+PG1mcmFjPjxtcm93Pjxtbz4mI3gyMjEyOzwvbW8+PG1uPjM8L21uPjwvbXJvdz48bW4+NDwvbW4+PC9tZnJhYz48bWk+eDwvbWk+PG1vPis8L21vPjxtbj4xPC9tbj48L21hdGg+v3S99wAAAABJRU5ErkJggg==)
Step 1 of 1:
We have given a line passes through a point (6, 6) and perpendicular to a line ![y equals fraction numerator negative 3 over denominator 4 end fraction x plus 1](data:image/png;base64,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)
Since product of two perpendicular lines is equal to -1.
So,
![m cross times fraction numerator negative 3 over denominator 4 end fraction equals negative 1](data:image/png;base64,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)
![m equals 4 over 3](data:image/png;base64,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)
Therefore the equation of the line will be
![y minus 6 equals 4 over 3 left parenthesis x minus 6 right parenthesis](data:image/png;base64,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)
![y equals 4 over 3 x minus 2](data:image/png;base64,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)
Therefore the equation of the line will be
Related Questions to study
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 2 semicolon a subscript 1 equals negative 1](data:image/png;base64,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)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript minus 2 semicolon a subscript 1 equals negative 1](data:image/png;base64,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)
Maths-General
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 6 semicolon a subscript 1 equals 9](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJcAAAARCAYAAADQdj68AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAoFJREFUeNrtWM9HZVEcv55kVtFiJLOIjDFajMjIeJLILJ4kkaTlI+kfmEVaJG1atkuLJIkkyWiXjFaRjLQYkVYtEi2SPM/j9fnyKXeOe3une+9559zrffgs7nHu9fn+OOf7vV/Pa8AWvoPb4ANYAvfB/pTZIHqPqf8J3AE7G6G1iykm0xc+t4CTDFRa8BO84CHJgU1gEfwHtjVCnCyqmvu6wNMM2HsackuNgUvqomTfPHgLlsG/YIcl4S5pSTq5VsCJDPim8oa+M3XxN7gMtnKD9AMjMZ1di2FIWotLySVlo11j3xa/OeJonK7AnoD1DvZfr5igSD/WwYKFILmkxURyldhr7TIIZZaYSY3kcsk3Uv6u2dTnyCHeWmX/xiPwh/LyH0vXrUtaTJz4KgNQYBMsQcmDl+BMynzTT00lUhL/s3pzPdFIf918tOR8E1pcurlk9PApYL0bvKnxrktxCsMH8MS/cKdsyAc1ZXWCbS1SsubYKJtIrgMlQfwoJ+ibqHbExQC44F+4Yca9QETtWEou21o2OIeqGkouKX3jAetf1RMf0zdR7YiLRfVmXuAvco71e5MnLOxvZ4hNqJy0XwmLc0WLqeRqZp9UZM8l6AXPwcEaDf17fBPVDl0cgqO0x2NCSbIPB22eZUM2x9NxG/CLm+N8Y4Mfkz7h3oBwF7SYPPEfwVX2SxUmW5/mKELHN/WwY5DNfIV9pOj99h4HqOj1/p8u55nBphFHS9RGtd7lJGzWVYjgG9fs0J5BrSvPaxnVYjsochNf+EpnWu3QhkyGp5XnYka12A6KlPq2DNihjV3lmt7z7E3OTWtJTVCyYse98iusPmdBS9whoktJZdWOZxjZ+uXylBiXAAABBnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtc3ViPjxtaT5hPC9taT48bWk+bjwvbWk+PC9tc3ViPjxtbz49PC9tbz48bXN1Yj48bWk+YTwvbWk+PG1yb3c+PG1pPm48L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjE8L21uPjwvbXJvdz48L21zdWI+PG1vPis8L21vPjxtbj42PC9tbj48bW8+OzwvbW8+PG1zdWI+PG1pPmE8L21pPjxtbj4xPC9tbj48L21zdWI+PG1vPj08L21vPjxtbj45PC9tbj48L21hdGg+zjvpZwAAAABJRU5ErkJggg==)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 6 semicolon a subscript 1 equals 9](data:image/png;base64,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)
Maths-General
Maths-
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 15 semicolon a subscript 1 equals 8](data:image/png;base64,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)
Write explicit formula. ![a subscript n equals a subscript n minus 1 end subscript plus 15 semicolon a subscript 1 equals 8](data:image/png;base64,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)
Maths-General
Maths-
Graph each function ![f left parenthesis x right parenthesis equals fraction numerator 4 x minus 3 over denominator x plus 8 end fraction](data:image/png;base64,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)
Graph each function ![f left parenthesis x right parenthesis equals fraction numerator 4 x minus 3 over denominator x plus 8 end fraction](data:image/png;base64,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)
Maths-General
Maths-
What is the graph of the function![f left parenthesis x right parenthesis equals fraction numerator 2 x plus 1 over denominator 3 x minus 4 end fraction](data:image/png;base64,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)
What is the graph of the function![f left parenthesis x right parenthesis equals fraction numerator 2 x plus 1 over denominator 3 x minus 4 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Write recursive formula and explicit formula. -15,-6,-3,12,21,...
Write recursive formula and explicit formula. -15,-6,-3,12,21,...
Maths-General
Maths-
The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is perpendicular to the north path.
The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is perpendicular to the north path.
Maths-General
Maths-
Write recursive formula and explicit formula. 62,57,52,47,42,...
Write recursive formula and explicit formula. 62,57,52,47,42,...
Maths-General
Maths-
Write recursive formula and explicit formula. -4, 5,14,23,32,...
Write recursive formula and explicit formula. -4, 5,14,23,32,...
Maths-General
Maths-
What are the vertical and horizontal asymptotes of the graph of each function?
![fraction numerator x squared plus 5 x plus 4 over denominator 3 x squared minus 12 end fraction](data:image/png;base64,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)
What are the vertical and horizontal asymptotes of the graph of each function?
![fraction numerator x squared plus 5 x plus 4 over denominator 3 x squared minus 12 end fraction](data:image/png;base64,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)
Maths-General
Maths-
The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.
The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.
Maths-General
Maths-
Write recursive formula and explicit formula. 12,19,26,33,40,...
Write recursive formula and explicit formula. 12,19,26,33,40,...
Maths-General
Maths-
What are the vertical and horizontal asymptotes of the graph of each function?
![G left parenthesis x right parenthesis equals fraction numerator 2 x squared plus x minus 9 over denominator x squared minus 2 x minus 8 end fraction](data:image/png;base64,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)
What are the vertical and horizontal asymptotes of the graph of each function?
![G left parenthesis x right parenthesis equals fraction numerator 2 x squared plus x minus 9 over denominator x squared minus 2 x minus 8 end fraction](data:image/png;base64,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)
Maths-General
Maths-
Are graphs of the equations parallel, perpendicular or neither?
![y equals negative 5 x space straight & space 25 x plus 5 y equals 1](data:image/png;base64,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)
Are graphs of the equations parallel, perpendicular or neither?
![y equals negative 5 x space straight & space 25 x plus 5 y equals 1](data:image/png;base64,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)
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 93,86,79,72,66,...
Tell whether the given sequence is an arithmetic sequence. 93,86,79,72,66,...
Maths-General