Question

write the equation of the line through the point (5,-3) and(4,-8)?
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Answer 1

Step-by-step explanation:

I have attached the solution above hope it helps.

Answer 2

$\rm \: Equation \: of \: line \: passing \: through \: points \: (x_1 , y_1) \: and \: (x_2 , y_2) : \\ \\ \\ \boxed{\rm\longrightarrow y - y_1 = (x-x_1)\bigg( \dfrac{y_2-y_1}{ x_2-x_1} \bigg )} \\ \\ \tt \rightarrow \: here \: \bigg( \dfrac{y_2-y_1}{ x_2-x_1} \bigg ) is \: slope \: of \: line$

Now , we have to find out the equation of the line through the point (5,-3) and (4,-8) :-

$\rm \longrightarrow \: y - ( - 3) = (x - 5)\bigg( \dfrac{ - 8-( - 3)}{4 - 5} \bigg ) \\ \\ \\ \rm \longrightarrow \: y + 3 = (x - 5)\bigg( \dfrac{ - 8 + 3}{ - 1} \bigg )\\ \\ \\ \rm \longrightarrow \: y + 3 = (x - 5)\bigg( \dfrac{ - 5}{ - 1} \bigg )\\ \\ \\ \rm \longrightarrow \: y + 3 = (x - 5){ 5} \\ \\ \\ \rm \longrightarrow \: y + 3 = 5x - 25\\ \\ \\ \rm \longrightarrow \: y + 3 - 5x + 25 = 0 \\ \\ \\ \rm \longrightarrow \: y - 5x + 28 = 0$