Question

write the equation of the line perpendicular to y= 5/2x+3 that passes through the point (-7,9). Type an answer using slope-intercept form or using the given points in point-slope form

Answer 1

Answer:

 5y = -2x + 31

Step-by-step explanation:

Given equation:

      y = $\frac{5}{2} x + 3$

Coordinate  = (-7,9)

Unknown:

Equation of the line perpendicular  = ?

Solution:

The slope - intercept format of a line is given as;

      y = mx + c

where y and x are the coordinates

           m is the slope

           c is the y-intercept

y = $\frac{5}{2} x + 3$

 From the given equation; slope is $\frac{5}{2}$

       

A line perpendicular will have a slope that is negative and the inverse of this;

      slope of perpendicular line  = $-\frac{2}{5}$

Since y= 9 and x = -7;

  So;

            9 = $\frac{-2}{5} x (-7)$ + C

            9 = $\frac{14}{5}$ + C

           C  = 9 - $\frac{14}{5}$   = $\frac{31}{5}$

Now,

       y  =  $-\frac{2}{5}$x +  $\frac{31}{5}$

mulitply through by 5;

     5y = -2x + 31