Question

find the slope-intercept equation of a line through (4,9) with slope 3/4

Answer 1

Answer:

y = ( 3 / 4 )x + 6.

Step-by-step explanation:

Equations are firstly written in the form of :  

      y - y₁ = m( x - x₁ )         { where m is the slope and ( x₁ , y₁ ) are two points on that line }

Here, that point is ( 4 , 9 ) and slope is 3 / 4  :

  Equation is given by :

⇒ ( y - 9 ) = ( 3 / 4 ) ( x - 4 )

⇒ 4( y - 9 ) = 3( x - 4 )

⇒ 4y - 36 = 3x - 12

⇒ 4y - 3x = 36 - 12

⇒ 4y - 3x = 24

⇒ 4y = 24 + 3x

⇒  y = ( 3x + 24 ) / 4

⇒ y = ( 3x / 4 ) + ( 24 / 4 )

⇒ y = ( 3 / 4 )x + 6

       This is in the form of slope-intercept.

Hence the required equation is y = ( 3 / 4 )x + 6.