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Sagot :
In this question, we use the slope equation and its further calculation can be defined as follows:
Slope equation [tex]=\bold{\frac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\to \bold{f(x)= y=\frac{2}{8-x}}\\\\\\\to \bold{P(9,-2)=(x_2,y_2)}\\\\\to \bold{q(x_1, f(x))}[/tex]
Calculating the Slope:
[tex]=\bold{\frac{-2-(\frac{2}{8-x})}{9-x}}[/tex]
[tex]=\bold{\frac{-16+2x-2}{(9-x)(8-x)}}\\\\=\bold{\frac{(2x-18)}{(9-x)(8-x)}}\\\\=\bold{\frac{-2(9-x)}{(9-x)(8-x)}}\\\\=\bold{\frac{-2}{(8-x)}}[/tex]
When
[tex]x=8.9\\\\m= \bold{\frac{-2}{(8-8.9)}} = \bold{\frac{-2}{(0.9)}}=-2.222222222[/tex]
When
[tex]x=8.99\\\\m= \bold{\frac{-2}{(8-8.99)}} = \bold{\frac{-2}{(0.99)}}=-2.020202020202[/tex]
When
[tex]x=8.999 \\\\m= \bold{\frac{-2}{(8-8.999)}} = \bold{\frac{-2}{(0.999)}}=-2.002002[/tex]
When
[tex]x=9.1\\\\m= \bold{\frac{-2}{(8-9.1)}} = \bold{\frac{-2}{-1.1}}=1.818181[/tex]
When
[tex]x=9.01\\\\m= \bold{\frac{-2}{(8-9.01)}} = \bold{\frac{-2}{-1.01}}=1.98019802[/tex]
When
[tex]x=9.001\\\\m= \bold{\frac{-2}{(8-9.001)}} = \bold{\frac{-2}{-1.001}}=1.998002[/tex]
When
[tex]x=9.0001\\\\m= \bold{\frac{-2}{(8-9.0001)}} = \bold{\frac{-2}{-1.0001}}=1.99980002[/tex]
For point b:
[tex]P(9, -2)\\\\m = 2[/tex]
For point c:
Line equation:
[tex]\to \bold{y= m(x- x_1)+y_1}\\\\\to \bold{y= 2(x-9)+(-2)}\\\\\to \bold{y= 2x-18-2}\\\\\to \bold{y= 2x-20}\\\\[/tex]
Learn more:
brainly.com/question/13219315
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