Question

Find the equation of line passing through(2, 5) and having slope −4 / 5.

a) 5x+4y-17=0

b) 4x+5y+17=0

c)4x-5y-17=0

d)4x+5y-33=0​

Answer 1

$\rm\large Equation \: of \: line \: passing \: through \: points \: (x_1 , y_1) \: and \: having \: slope \: m_1 :$

$\boxed{\tt \large ( y - y_1) =( x-x_1)m_1}$

Therefore, the equation of line passing through(2, 5) and having slope −4 / 5 :-

$\rm \implies y - 5 = (x - 2)( \dfrac{ -4 }{5} ) \\ \\ \rm \implies( y - 5 )(5)= (x - 2)({ -4 })\\ \\ \rm \implies5 y - 25={ -4x } + 8\\ \\ \rm \implies5 y - 25 + 4x - 8 = 0\\ \\ \rm \implies5 y - 25 + 4x - 8 = 0\\ \\ \rm \implies5 y + 4x - 33= 0$

Answer :

Option (d)4x+5y-33=0 is correct

Additional Information :-

$\rm\: Equation \: of \: line \: passing \: through \: points \: (x_1 , y_1) \: and \: (x_2 , y_2) :$

$\boxed{ \tt y - y_1 = x-x_1\bigg( \dfrac{y_2-y_1}{ x_2-x_1} \bigg )}$

$\tt \rightarrow \: here \: \bigg( \dfrac{y_2-y_1}{ x_2-x_1} \bigg ) is \: slope \: of \: line.$

Answer 2

Answer:

Given :-

• A line passing through (2 , 5) and having slope -4/5.

To Find :-

• What is the equation.

Formula Used :-

$\mapsto$ Equation of a line is :

$\bigstar \: \boxed{\sf{(y - y_1) =\: m_1(x - x_1)}}$

Solution :-

Given :

• x₁ = 2
• y₁ = 5
• m₁ = $\sf \dfrac{- 4}{5}$

Then, according to the question by using the formula we get,

↦ $\sf y - 5 =\: \dfrac{- 4}{5} \times (x - 2)$

↦ $\sf (y - 5) \times 5 =\: - 4 \times (x - 2)$

↦ $\sf 5y - 25 =\: - 4x + 8$

↦ $\sf 4x + 5y - 25 - 8 =\: 0$

➠ $\sf\bold{\red{4x + 5y - 33 =\: 0}}$

$\therefore$ The equation is 4x + 5y - 33 = 0.

Hence, the correct options is option no d) 4x + 5y - 33 = 0.