Question

What is the equation of the line which passes through the points ( 1, 18 ) and ( -2 , 9 ) ?

Please give me the answer as soon as possible.

Answer 1

Answer:

Given:-

What is the equation of the line which passes through points ( 1, 18 ) and ( - 2, 9 ) ?

To Find:-

Equation of the line.

Note:-

●》Here, we will first find Slope of a line i.e. $Slope ( m ) = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

●》Here, $(x_{1}, y_{1} ) = Coordinate \ \ of \ \ first \ \ point \ \ of \ \ line.$

$( x_{2}, y_{2} ) = Coordinate \ \ of \ \ second \ \ point \ \ of \ \ line.$

●》After finding Slope ( m ), Equation of a line = $( y - y_{1} ) = m ( x - x_{1} )$ .

Solution:-

$\huge\red{Points \ \ are = ( 1, 18 ) \ \ and \ \ ( -2, 9 )}$

$\huge\red{ \ \ The \ \ equation \ \ of \ \ line = ?}$

☆ According to note first point~

▪︎$Slope ( m ) = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}$

☆ According to note second point $( x_{1}, y_{1} = 1, 18 ; x_{2}, y_{2} = -2, 9 )$ ( respectively ), So~

▪︎$Slope ( m ) = \dfrac{( 9 - 18 )}{( -2 - 1 )}$

▪︎$Slope ( m ) = \cancel\dfrac{( -9 )}{( - 3 )}$

▪︎$Slope ( m ) = 3$

_____________________________________________

[ Now, we will find equation of a line ]

☆ According to note third point $( x_{1} = 1, y_{1} = 18, Slope ( m ) = 3 )$ ~

▪︎$( y - y_{1} ) = m ( x - x_{1} )$

▪︎$( y - 18 ) = 3 ( x - 1 )$

☆ Multiplying "3" inside the bracket~

▪︎$( y - 18 ) = ( 3 × x - 3 × 1 )$

▪︎$( y - 18 ) = ( 3x - 3 )$

☆ Transposing [ ( 3x - 3 ) ] to other side~

▪︎$( y - 18 ) - ( 3x - 3 ) = 0$

☆ Opening brackets by multiply sign inside it~

▪︎$y - 18 - 3x + 3 = 0$

▪︎$y - 3x -18 + 3 = 0$

▪︎$y - 3x - 15 = 0$

$\huge\pink{The \ \ equation \ \ of \ \ line = y - 3x - 15 = 0}$

Answer:-

Hence, the equation of the line $\implies y - 3x - 15 = 0$ .

:)

Answer 2

What is the equation of the line which passes through the points ( 1, 18 ) and ( -2 , 9 ) ?

Please give me the answer as soon as possible.