through (9,4) and perpendicular to 3x-y=7

Question

the question is asking to find the equation written in slope intercept form that passes through (9,4)

Answer 1

perpendicular to 3x-y=7

 

first we write this equation in slope intercept form

 

y=3x-7

 

so slope = 3

 

So slope of line perpendicular to this line is =-1/3

 line goes through (9,4)

 

first we write equation in point slope form

 

y-y1=m(x-x1)

 

y-4=-1/3(x-9)

 

3(y-4)=-1(x-9)   ______ multiplied both side with 3

3y-12=-x+9       ______  distribute

 

3y=-x+21      _______ add 12 to both side

 

y=-1/3x +21/3  ______ divide both side with 3

 

y=(-1/3) x + 7   ________slope intercept form

 

 

 

Answer 2

Slope of line 3x-y=7 > y=3x-7 > slope m1=3

If slope of a line perpendicular to above is m2, them m2*m1=-1 > m2=-1/m1=-1/3

 

So equation of the second line y=m2x+c >y=-1/3x+c

since it passes through 9,4, then 4=-1/3*9+c , so c=7

 

So the equation of the second line y=-1/3x+7