Question

Give the slope-intercept form of the equation of the line that is perpendicular to 7x + 3y = 18 and contains P(6, 8).

Answer 1

Rearrange the equation into slope intercept form

7x+3y=18

3y=-7x+18

y=-7x/3+18/3 so the slope of the reference line is -7/3

To be perpendicular to this line the slope must be the negative reciprocal of this...mathematically m1*m2=-1.  So the slope of our perpendicular line is:

-7m/3=-1

-7m=-3

m=3/7 so our line so far is:

y=3x/7+b, using point (6,8) we can solve for b, the y-intercept

8=3(6)/7+b

8=18/7+b

56/7-18/7=b

38/7=b so our line is:

y=3x/7+38/7 or if you prefer

y=(3x+38)/7