a line has a slope of $-\\frac{1}{3}$ and passes through the point $(-12,14)$. write its equation in slope…

a line has a slope of $-\\frac{1}{3}$ and passes through the point $(-12,14)$. 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 $-\\frac{1}{3}$ and passes through the point $(-12,14)$. write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer

Explanation:

Step1: Write the point - slope form

The point - slope form of a line is (y - y_1=m(x - x_1)), where (m) is the slope and ((x_1,y_1)) is a point on the line. Given (m =-\frac{1}{3}), (x_1=-12), and (y_1 = 14), we have (y-14=-\frac{1}{3}(x + 12)).

Step2: Simplify to slope - intercept form

[ \begin{align*} y-14&=-\frac{1}{3}x-4\ y&=-\frac{1}{3}x-4 + 14\ y&=-\frac{1}{3}x+10 \end{align*} ]

Answer:

(y =-\frac{1}{3}x + 10)