Question is in description.

Question

Find the equation for the line that passes through the point (3, 4), and that is perpendicular to the line with the equation 9/4x − 3y = 39/4.

Answer 1

Hi Shatoria,

 

The product of the slope of perpendicular lines is minus one (- 1)

m1*m2= -1

Equation of line 1 is 

94x - 3y =394, rewrite in standard slope intercept form

-3y = -94x + 394     divide both sides by - 3

   y = (94/3)x +394/3

m1 = 94/3 use this in the slope equation above

(94/3)*m2 = -1

m2 = -3/94 so the equation of the perpendicular line is

y =(-3/94)x + c  To find c we know that the line passes through the point (3,4), plug it in the equation

4 = (-3/94)(3) +c

4 = -9/94 + c

4+ 9/94 =c    which gives  c =385/94

 

y = (-3/94)x +385/94

94y = -3x +385  or       3x + 94y = 385

 

Answer 2

1.  from the equation given, find its slope  m (by solving for y, you'll produce y = mx + b)

2.  any line perpendicular to that would have slope = negative reciprocal of "m" obtained in step 1

3. the line that you're interested in also has an equation y = mx + b (using the result of step 2 for this new slope)

4. You know that (3, 4) satisfies the equation in step 3; plug in x = 3, y = 4 and you'll be able to solve for the "b" value for the desired line.