Write the equatiion of the line that passes through (-1,3) that is perpendicular to the line y = -1/4x+4

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The product of the slope of two perpendicular lines is -1. The slope of the line y = (-1/4)x + 4 is (-1/4), a line perpendicular to this line has a slope of 4.

As the required line passes through the point (-1, 3)

(y - 3)/(x + 1) = 4

=> y - 3 = 4x + 4

=> 4x - y + 7 = 0

The equation of the line perpendicular to y = (-1/4)x + 4 and passing through the point (-1, 3) is 4x - y + 7 = 0

jana-96's profile pic

jana-96 | Student, Grade 10 | eNotes Newbie

Posted on

because they are perpendicular the slope of the line is 4.
let's call the slope of the first line is m1 (which is -1/4) and the slope of the second line is m2 (which is 4)
              m1*m2=-1
              (-1/4)*m2=-1
               m2=4
              y=m2x+n
              => y=4x+n
we know that this line (the second one) passes through (-1,3)
=> 3=4*(-1)+n
     3=-4+n
     n=7
=>y=4x+7

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