# What are the intercepts of -7y=3y-2(x-9) -x^2?

Jun 6, 2018

$x = - 10 \pm \sqrt{19}$

$y = - \frac{9}{5}$

#### Explanation:

To find the y-intercepts set x=0 and solve for y:

$- 7 y = 3 y - 2 \left(x - 9\right) - {x}^{2}$

$- 7 y = 3 y - 2 \left(0 - 9\right) - {0}^{2}$

$- 7 y = 3 y - 2 \left(- 9\right)$

$- 7 y = 3 y + 18$

$- 7 y = 3 y + 18$

$- 10 y = 18$

$y = - \frac{9}{5}$

To find the x-intercept(s) if they exist set y=0 and solve for x:

$- 7 y = 3 y - 2 \left(x - 9\right) - {x}^{2}$

$- 7 \left(0\right) = 3 \left(0\right) - 2 \left(x - 9\right) - {x}^{2}$

$0 = - 2 \left(x - 9\right) - {x}^{2}$

$0 = - {x}^{2} - 2 \left(x - 9\right)$

$0 = - {x}^{2} - 2 x + 18$

$0 = {x}^{2} + 2 x - 18$

You will need to complete the square or use the quadratic equation to find these roots:

$x = - 10 \pm \sqrt{19}$

graph{-7y=3y-2(x-9) -x^2 [-20.58, 19.42, -4.8, 15.2]}