# Math Help - Finding equation of a line

1. ## Finding equation of a line

i don't understand this AT ALL. oh calculus.
would it be 10x-5, while 10 is the slope...gah i have no clue X_X plz help

Find an equation of the line that is both normal to the given parabola and also parallel to the given line

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

2. $y = 5x^2 - 5x + 6$

$y' = 10x - 5$

the gradient function is 10x - 5.

the line
$x - 5y = 6$
$x - 6 = 5y$
$\frac{x}{5}- \frac{6}{5} = y$

the gradient of the wanted line must be 6/5, and hence 6/5 is the normal to the parabola. the gradient of the tangent to the parabola must therefore be -5/6

$\frac{-5}{6}= 10x - 5$

Solve for x

$4\tfrac{1}{6} = 10x$

$x= \frac{5}{12}$

when $x= \frac{5}{12}$ $y = 4\tfrac{113}{144}$

Equation of the line

$\frac{y - 4\tfrac{113}{144}}{x - \frac{5}{12}} = \frac{6}{5}$