5x-5y/4=4x-4/2 Find the equation of the line which passes through the point (10,7) and is perpendicular to the given line. Express in slope intercept form.

Question

5x-5y/4=4x-4/2 Find the equation of the line which passes through the point (10,7) and is perpendicular to the given line. Express in slope intercept form.

Answer 1

5x-5y/4 = 4x-4/2 solve for y

20x-5y = 16x -8

5y = 4x+8

y = 4x/5 +8/5 has slope = 4/5 = coefficient of the x term

perpendicular line has the negative inverse slope -5/4

y = -5x/4 + b Plug in (10,7) to find b

7 = -50/4 + b

b = 7+25/2 = 39/2

y = -5x/4 + 39/2 is the perpendicular line through the given point

UNLESS you may have intended the problem as (5x -5y)/4 = (4x-4)/2= 2x-2

then 5x-5y = 8x-8

5y = -3x +8

y = -3x/5 +8/5 which has slope = -3/5

perpendicular line = 5/3

y = 5x/3 +b

7 = 50/3+b

b = 7-50/3 = -29/3

y = 5x/3 -29/3 is the perpendicular line through (10,7)