a line has a slope of $\\frac{1}{3}$ and passes through the point $(-15,7)$. write its equation in slope…

a line has a slope of $\\frac{1}{3}$ and passes through the point $(-15,7)$. 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 $(-15,7)$. 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) is the slope and ((x_1,y_1)) is a point on the line. Given (m = \frac{1}{3}), (x_1=-15), and (y_1 = 7), we substitute these values into the formula: (y - 7=\frac{1}{3}(x+15))

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

First, distribute (\frac{1}{3}) on the right side: (y-7=\frac{1}{3}x+5) Then, add 7 to both sides of the equation: (y=\frac{1}{3}x+5 + 7) (y=\frac{1}{3}x+12)

Answer:

(y=\frac{1}{3}x + 12)