Question

A line is represented by y = 4x + 3. A perpendicular line goes through (8,5). What would be the slope intercept form for the perpendicular
line?

Answer 1

Answer:

 y  =  $-\frac{1}{4}$x + 7

Step-by-step explanation:

Given expression:

             y  = 4x + 3

 Coordinate = (8,5)

Unknown:

The equation of a line perpendicular = ?

Solution:

A line perpendicular will have slope that is the negative inverse of the one given.

       Equation of a straight line;

                       y  = mx + c

  y and x are the coordinates

    m is the slope

   c is the y- intercept

For  y  = 4x + 3;

          slope is 4;

A perpendicular line will have a slope of $-\frac{1}{4}$

Let us find the y-intercept of the new line;

               y  = 5, x  = 8

             5 = $-\frac{1}{4}$ x 8 + c

             5 = -2 + c

             c  = 7

the equation of the line perpendicular is;

             y  =  $-\frac{1}{4}$x + 7