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

Answer: y=-0.4x+20.2

Explanation:

`5x-2y=6\\5x-2y+2y=6+2y\\5x=6+2y\\5x-6=6+2y-6\\5x-6=2y`

Divide both parts of the equation by 2:

`\displaystyle\\(5x-6)/(2)=y\\\\(5)/(2) x-3=y`

Coordinates of the intersection point of the equations:

`\displaystyle\\y=(5)/(2)x-3 \ and\ x=8\ are:`

`\displaystyle\\x=8\\Hence,\\y=(5)/(2) (8)-3\\\\y=(5*8)/(2) -3\\\\y=(5*4*2)/(2)-3\\\\y=5*4-3 \\\\y=20-3\\\\y=17\\Thus, (8,17)`

`\displaystyle\\The\ slope\ \perp=-(1)/((5)/(2) ) \\\\The\ slope\ \perp=-(2)/(5)`

`\displaystyle\\-(2)/(5) =(y-17)/(x-8)`

Multiply both parts of the equation by (x-8):

`\displaystyle\\-(2)/(5)(x-8)=y-17\\\\-(2)/(5) x+(2*8)/(5) =y-17\\\\-(2)/(5)x+(16)/(5) =y-17\\\\ -0.4x+3.2=y-17\\\\ -0.4x+3.2+17=y-17+17\\\\-0.4x+20.2=y`-