Homework Help

What is the equation of the line that intesects 3x + 4y = 8 at (0, 2) and is...

user profile pic

b52 | Student, Grade 9 | eNoter

Posted June 29, 2012 at 4:53 PM via web

dislike 3 like

What is the equation of the line that intesects 3x + 4y = 8 at (0, 2) and is perpendicular to it.

2 Answers | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 29, 2012 at 4:58 PM (Answer #1)

dislike 0 like

The product of the slope of two perpendicular lines is equal to -1. The line 3x + 4y = 8 can be written in the slope intercept form as y = (-3/4)x + 2

As the slope of this line is -3/4, the slope of the required line that is  perpendicular to it is 4/3. As the required line intersects at (0, 2), the equation of the line is (y - 2)/x = 4/3

=> 3y - 6 = 4x

=> 4x - 3y + 6 = 0

The line 4x - 3y + 6 = 0 is perpendicular to 3x + 4y = 8 and intersects it at (0, 2).

user profile pic

vaaruni | High School Teacher | Salutatorian

Posted June 30, 2012 at 6:59 AM (Answer #2)

dislike 0 like

The given line AB is  3x + 4y = 8 

                   Or,  4y = -3x + 8

                   Or,   y= (-3/4) x + 8 

   Therefore the slope of the line m1 = -3/4  [since, y = mx + c ]

  It is given that the require lie is perpendicular to the line AB.         i.e.  m1*m2 = -1  [ where m2 is the slope of the require line ] 

  m2 = (-1)/m1 = (-1)/(-3/4) = 4/3

  m2 = 4/3 --------(2) 

 Next It is stated that the require line intersect the given line AB at (0,2) Which means y-interxept (c) of the require line is 2  i.e. c=2

therefore the equation of the require line ----->

   y = (4/3)x + 2  [ substituting the value of the slope m and the                                  y- intercept (c) in the  equation : y = mx + c ]

Or,    y = (4x + 6)/3 

Or,    3y = 4x + 6

Or,    3y - 4x -6 =0

Hence equation of the require line --->3y - 4x - 6 = 0 Answer         

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes