Homework Help

What is the equation of a line perpendicular to 8y-2x=-6 and also passing through the...

user profile pic

paul1234 | Student | eNoter

Posted May 3, 2011 at 3:25 PM via web

dislike 1 like

What is the equation of a line perpendicular to 8y-2x=-6 and also passing through the point (2,3).

Tagged with line, math

2 Answers | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 3, 2011 at 3:32 PM (Answer #1)

dislike 0 like

The product of the slope of perpendicular lines is -1. First find the slope of the given line.

8y - 2x = -6

=> 8y = 2x - 6

=> y = x/4 - 3/4

This is in the slope-intercept form y = mx + c where m is the slope.

The slope is 1/4. As a line perpendicular to this line has a slope which is the negative reciprocal, the slope of the required line is -4. The line also passes through (2,3)

The equation of the line is : (y - 3)/(x - 2) = -4

=> y - 3 = -4x + 8

=> 4x + y - 11 = 0

The equation of the required line is 4x + y - 11 = 0

user profile pic

academicsfirst | High School Teacher | (Level 2) Adjunct Educator

Posted May 3, 2011 at 7:50 PM (Answer #2)

dislike 0 like

We are asked to find the equation of a line perpendicular to

8y-2x = -6 which passes through the point (2,3).

We begin by finding the slope of the given line.  We will convert the given equation to slope-intercept form.

=>8y - 2x = -6

=> 8y = 2x - 6

=> y = 2/8 x - 6/8

=> y = 1/4 x - 3/4

The slope of a line perpendicular to the above equation would be -4.

We substitute -4 as the perpendicular slope and the given point (2,3) into the slope intercept form to find "b."

=>y = mx + b

=> 3 = -4(2) + b

=> 3 = -8 + b

=> 11 = b

We now have the slope and the y intercept for the equation of the perpendicular line.

Substitute our values into the slope intercept form.

y = mx + b

y = -4x + 11.

The answer is y = -4x + 11 (slope-intercept form).  The standard form of the answer is 4x + y = 11.

 

 

 

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes