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Art [367]
3 years ago
14

Find an equation of the line that goes through the points (10,34) and (-1,10)

Mathematics
1 answer:
kotykmax [81]3 years ago
3 0

Answer:

Given points are ( 10 ,34 ) and ( -1 , 10)

Step-by-step explanation:

<em>The </em><em>equation</em><em> </em><em>of </em><em>line </em><em>is </em><em>given </em><em>by </em>

<em>first </em><em>we </em><em>can </em><em>find </em><em>slope </em><em>(</em><em>m</em><em>) </em>

<em>=</em><em> </em><em>(</em><em>y2 </em><em>-</em><em> </em><em>y</em><em>1</em><em>)</em><em> </em><em>/</em><em> </em><em>(</em><em> </em><em>x2</em><em> </em><em>-</em><em> </em><em>x1</em><em>)</em>

<em>=</em><em> </em><em>3</em><em>4</em><em>-</em><em>1</em><em>0</em><em>/</em><em>1</em><em>0</em><em>+</em><em>1</em>

<em> </em><em>=</em><em>2</em><em>4</em><em>/</em><em>1</em><em>1</em>

<em>Now </em><em>the </em><em>equation </em><em>is</em>

<em>y </em><em>-</em><em> </em><em>y1 </em><em>=</em><em> </em><em>m </em><em>(</em><em> </em><em>x </em><em>-</em><em> </em><em>x1) </em>

<em>y </em><em>-</em><em> </em><em>1</em><em>0</em><em> </em><em>=</em><em> </em><em>2</em><em>4</em><em>/</em><em>1</em><em>1</em><em> </em><em>(</em><em> </em><em>x </em><em>+</em><em>1</em><em>1</em><em>)</em>

<em>11 </em><em>(</em><em> </em><em>y </em><em>-</em><em> </em><em>1</em><em>0</em><em> </em><em>)</em><em> </em><em>=</em><em> </em><em>2</em><em>4</em><em> </em><em>(</em><em>x </em><em>+</em><em> </em><em>1</em><em>1</em><em>)</em>

<em>11y </em><em>-</em><em> </em><em>1</em><em>1</em><em>0</em><em> </em><em>=</em><em> </em><em>24x </em><em>+</em><em> </em><em>2</em><em>6</em><em>4</em>

<em>24x </em><em>+</em><em> </em><em>2</em><em>6</em><em>4</em><em> </em><em>+</em><em>110-11y </em><em>=</em><em>0</em>

<em>24x </em><em>-</em><em> </em><em>11y </em><em>+</em><em> </em><em>3</em><em>7</em><em>4</em><em> </em><em>=</em><em> </em><em>0</em>

<em>which </em><em>is </em><em>the </em><em>required </em><em>equation </em>

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\displaystyle\bf\\2)\\A_{61}=a_1+(61-1)\times r=-113+60\times5=-113+300=187\\\\S_{61}=(-113)+(-108)+(-103)+...+(-8)+(-3)+2+7+12+...+187\\\\S_{61}=SA+SB\\\\SA=(-113)+(-108)+(-103)+...+(-8)+(-3)=-(3+8+103+108+113)\\\\n=\frac{113-8}{5}+1=\frac{105}{5}+1=21+1=22~terms\\SA=-\Big( \frac{n(113+3)}{2} \Big)=-\Big( \frac{22\times116}{2} \Big)=-11\times116 =-1276

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\displaystyle\bf\\SB=2+7+12+...+187\\\\n=\frac{187-2}{5}+1=\frac{185}{5}+1=37+1=38~terms\\\\SB=\frac{n(187+2)}{2}=\frac{38\times189}{2}=19\times189=3591\\\\S_{61}=SA+SB=-1276+3591=2315\\\\\boxed{\bf S_{61}=2315}    

 

 

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