Find the equation of the line through the point 6 1 and perp

Find the equation of the line through the point (6, 1) and perpendicular to the graph of the line 3x + 2y = 14. Write the equation in slope intercept form.

Solution

line perpendicular to the graph of the line 3x + 2y = 14.

2y+3x = 14 ---> y =-3x/2 +7 ;m=-3/2

So, slope of the line passing through(6, -1) is m = 2/3

Slope intercept form: y =mx+c

y = 2x/3 +c. Now find c

-1 = 2*6/3 +c---> c =-5

y = 2x/3 -5