Please need help

Question

(1 point) Find an equation for the linear function g(x) which is perpendicular to the line 5x−2y=6 and intersects the line 5x−2y=6 at x=8.

g(x)=

Answer 1

5x-2y = 6 has slope = 5/2. a perpendicular line has a negative inverse slope = -2/5

y = (-2/5)x + b where b is the y intercept

5x-2y = 6 at x = 8 is 5(8)-2y = 6

40-2y = 6

-2y =6-40 =-34

y = 17

plug x= 8 and y=17 into to y=(-2/5)x +b to solve for b

17 = (-2/5)8 +b

b = 17+16/5 = 85/5 +16/5 = 101/5

y =(-2/5)x + 101/5 is the perpendicular line intersecting the original line where x=8