Determine the equation of a line that is perpendicular to y=1/3x+6 that passes through the point (9,1)

Question

Y=Cvbvcc nbnjnnnnbbbbhhhbbbbbbb

Answer 1

Hi

 The slope of the line will be  m= -3 

So equation will be 

y= -3x +c

as it passes through

(9,1)

1= -3*9 + c

c= 28

 So equation of line is  

y= -3x+28

Answer 2

First, we must realize the slopes of perpendicular lines are negative reciprocals. 

Second, the equation of a line is in the form of  y=mx+b  where m is the slope and b is the y-intercept.

Therefore, in the original equation, y=(1/3)x + 6, m (the slope) is 1/3. Because the negative reciprocal of this is the slope of the perpendicular line, m = -3/1 or -3.

 Now we have y = -3x + b and must find b. Use the point given, (9,1), to solve for b.

                     y = -3x + b   original equation

                     1 = -3(9) + b  replacing (x,y) with (9,1)

                     1 = -27 + b  multiply

                     1 + 27 = b  add 27 to both sides

                           28 = b  solve for b

Now we know m & b for the perpendicular line. Just need to put those numbers in the equation of a line and we're done:

                            y = mx + b  equation of a line

                            y = -3x + 28   answer!