Question

what is the equation the two points which is on the line are: (17, 5) (1032​

Answer 1

Question:

What is the equation the two points which is on the line are: ( 17 , 5 ) , ( 10 , 32 ) .

To find:

$\bigstar To \: find \: equation.$

Answer:

$The \: equation \: is \: \underline{ \: \sf \red{27x + 7y - 494 = 0} \: }$

Given:

$\bigstar Points \: are \: given,$

$( 17 , 5 ), \: (10,32)$

$x _{1} = 17 , \: y _{1} = 5$

$x _{2} = 10 , \: y _{2} = 32$

Step-by-step explanation:

If the points are given, the equation will be

$\boxed{\frac{y - y _{1} }{x - x _{1} } = \frac{y_{2} - y_{1} }{x _{2} - x _{ 1 } }}$

$\implies \frac{y - 5}{x - 17} = \frac{32 - 5}{10 - 17}$

$\implies - 7(y - 5) = 27(x - 17)$

$\implies - 7y + 35 = 27x - 459$

$\implies 27x + 7y - 459 - 35 = 0$

$\implies \boxed{27x + 7y - 494 = 0}$

$\therefore \: the \: equation \: is \: \underline{ \: \sf \pink{\bold{27x + 7y - 494 = 0}} \: }$

More information:

★ One point form

$\boxed{y - y _{1} = m(x - x _{1}}$

★ Two point form

$\boxed{\frac{y - y _{1} }{x - x _{1} } = \frac{y_{2} - y_{1} }{x _{2} - x _{ 1 } }}$

★ Slope m

$\boxed{m = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }$