Turito Academy

Test Prep

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Step by step solution: Let the given points be denoted by (a, b) = (-3, -6) (c, d) = (2, 34) The equation of a line passing through two points  and  is <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator y minus d over denominator d minus b end fraction equals fraction numerator x minus c over denominator c minus a end fraction" width="109" height="36" style="vertical-align:-13px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»y«/mi»«mo»§#8722;«/mo»«mi»d«/mi»«/mrow»«mrow»«mi»d«/mi»«mo»§#8722;«/mo»«mi»b«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»§#8722;«/mo»«mi»c«/mi»«/mrow»«mrow»«mi»c«/mi»«mo»§#8722;«/mo»«mi»a«/mi»«/mrow»«/mfrac»«/math»'/> Using the above points, we have <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator y minus 34 over denominator 34 minus left parenthesis negative 6 right parenthesis end fraction equals fraction numerator x minus 2 over denominator 2 minus left parenthesis negative 3 right parenthesis end fraction" width="171" height="37" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»y«/mi»«mo»§#8722;«/mo»«mn»34«/mn»«/mrow»«mrow»«mn»34«/mn»«mo»§#8722;«/mo»«mo»(«/mo»«mo»§#8722;«/mo»«mn»6«/mn»«mo»)«/mo»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»§#8722;«/mo»«mn»2«/mn»«/mrow»«mrow»«mn»2«/mn»«mo»§#8722;«/mo»«mo»(«/mo»«mo»§#8722;«/mo»«mn»3«/mn»«mo»)«/mo»«/mrow»«/mfrac»«/math»'/> Simplifying the above equation, we have   <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator y minus 34 over denominator 34 plus 6 end fraction equals fraction numerator x minus 2 over denominator 2 plus 3 end fraction" width="118" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»y«/mi»«mo»§#8722;«/mo»«mn»34«/mn»«/mrow»«mrow»«mn»34«/mn»«mo»+«/mo»«mn»6«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»§#8722;«/mo»«mn»2«/mn»«/mrow»«mrow»«mn»2«/mn»«mo»+«/mo»«mn»3«/mn»«/mrow»«/mfrac»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="not stretchy rightwards double arrow fraction numerator y minus 34 over denominator 40 end fraction equals fraction numerator x minus 2 over denominator 5 end fraction" width="137" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo stretchy=¨false¨»§#8658;«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»§#8722;«/mo»«mn»34«/mn»«/mrow»«mn»40«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»§#8722;«/mo»«mn»2«/mn»«/mrow»«mn»5«/mn»«/mfrac»«/math»'/> Cross multiplying, we get 5(y - 34) = 40(x - 2) Expanding the factors, we have 5y - 170 = 40 x -80 Taking all the terms in the left hand side, we have -40x + 5y - 170 + 80 = 0 Finally, the equation of the line is -40x + 5y - 90=0 Dividing the equation throughout by(- 5), we get This is the required equation.   .

Determine the equation of the line that passes through <img src="data:image/png;base64,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" class="Wirisformula" alt="left parenthesis negative 3 comma negative 6 right parenthesis text  and  end text left parenthesis 2 comma 34 right parenthesis" width="151" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»§#8722;«/mo»«mn»3«/mn»«mo»,«/mo»«mo»§#8722;«/mo»«mn»6«/mn»«mo»)«/mo»«mtext»§#160;and§#160;«/mtext»«mo»(«/mo»«mn»2«/mn»«mo»,«/mo»«mn»34«/mn»«mo»)«/mo»«/math»'/>

Solution for the question - determine the equation of the line that passes through (-3,-6) and (2,34)