find an equation of the line. write the equation using function notation. through (7,-3) and perpindicular to 9y=x-18.

find an equation of the line. write the equation using function notation. through (7,-3) and perpindicular to 9y=x-18.

$$9y=x-18 \quad \small{\text{ or }} \quad y = \frac{1}{9}x - 2 \quad \small{\text{ the slope = }} m = \frac{1}{9}$$

$$\small{\text{the slope of the perpindicular line = }} m_{\perp} = -\frac{1}{m} = -\dfrac{1}{ \frac{1}{9} } = -9$$

$$\small{\text{the function of the perpindicular line = }} f(x) = y = m_{\perp}(x-x_p)+y_p$$

$$\\\small{\text{with point }} x_p = -3 \small{\text{ and }} y_p = 7 }} \small{\text{, }} f(x) = y = -9 [x-(-3)]+7 \\ y= -9(x+3)+7 \\ y= -9x-27+7 \\ \boxed{y= -9x -20}$$