Question

write the equation of the line in point - slope form using the indicated point. the equation of the line is $y + 9=-\frac{2}{3}(x - 6)$. (simplify your answer. type an equation. type your answer in point - slope form. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.

Step2: Identify the point and slope

We are given the point $(6,-9)$ and the equation $y + 9=-\frac{2}{3}(x - 6)$. Here $x_1 = 6$, $y_1=-9$ and $m=-\frac{2}{3}$. The equation is already in point - slope form as it follows the pattern $y - y_1=m(x - x_1)$ (in this case $y-(-9)=-\frac{2}{3}(x - 6)$ which simplifies to $y + 9=-\frac{2}{3}(x - 6)$).

Answer:

$y + 9=-\frac{2}{3}(x - 6)$