The graph of f passes through (1,9) and is perpendicular to the line whose equation is x=19. The equation of the function is....?

Answer 1

Greetings! Lets solve this shall we ?

So, we must find the equation of a line that passes through the point (1,9) and is perpendicular to x = 19. Then, we yield the equation of point-slope such that

y - y1 = m(x - x1), where (x1, y1) = (1,9) and x = 19 such that

y - 9 = m(19-1). Then

y - 9 = 18m

y = 18m + 9. Now we use the y-value and x = 19 to create

y = mx+b

y = 19m + 1. Now we set the two equations equal to each other to find the slope such that

18m + 9 = 19m + 1................Then subtract 18m from both sides

9 = m + 1............ Then subtract 1 to get

m = 8

Now bring back the point-slope form to obtain the function f such that

y - y1 = m(x - x1)

y - 9 = 8(x - 1)

y - 9 = 8x - 8

y = 8x + 1

I hope this helped!