Question

Complete the point-slope equation of the line through (3,6)(3,6)left parenthesis, 3, comma, 6, right parenthesis and (5,-8)(5,−8)left parenthesis, 5, comma, minus, 8, right parenthesis.

Use exact numbers.

Answer 1

$Let \: A(x_{1} , y_{1}) = ( 3,6 ) \:and \\B(x_{2} , y_{2}) = ( 5,-8 )$

$Slope \: of \: a \: line \: AB (m)\\ = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\= \frac{-8-6}{5-3} \\= \frac{-14}{2} \\= -7$

/* Point - Slope form : */

$\boxed { \pink { y - y_{1} = m(x-x_{1})}}$

$\implies y - 6 = (-7)(x - 3)$

$\implies 7(x-3)+ y - 6 = 0$

$\implies 7x - 21 + y - 6 = 0$

$\implies 7x + y - 27 = 0$

Therefore.,

$\red { Required \: equation : }\\\green{\: 7x + y - 27 = 0 }$

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Answer 2

Answer:

-7(x-3)

Step-by-step explanation:

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