a line has a slope of $-\\frac{4}{5}$ and passes through the point $(-12,9)$. write its equation in slope…

a line has a slope of $-\\frac{4}{5}$ and passes through the point $(-12,9)$. write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

a line has a slope of $-\\frac{4}{5}$ and passes through the point $(-12,9)$. write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer

Explanation:

Step1: Use the point - slope form

The point - slope form of a line is (y - y_1=m(x - x_1)), where (m =-\frac{4}{5}), (x_1=-12), and (y_1 = 9). Substitute these values into the formula: (y - 9=-\frac{4}{5}(x+12)).

Step2: Simplify to slope - intercept form ((y=mx + b))

[ \begin{align*} y-9&=-\frac{4}{5}x-\frac{48}{5}\ y&=-\frac{4}{5}x-\frac{48}{5}+9\ y&=-\frac{4}{5}x-\frac{48}{5}+\frac{45}{5}\ y&=-\frac{4}{5}x-\frac{3}{5} \end{align*} ]

Answer:

(y =-\frac{4}{5}x-\frac{3}{5})