Write the equation of a line in slope intercept form perpendicular to y=3x-5 passing through the point (-6,-2)

1. Given the slope of the original line m_1 = 3 , find the slope of the perpendicular line m_2 = -\frac{1}{3} .

2. Using the point (−6, −2) and the formula for a line y = mx + b , plug in the point and the new slope:

-2 = -\frac{1}{3}(-6) + b

3. Solve for b :

-2 = 2 + b

b = -4

4. The equation of the line in slope-intercept form is:

y = -\frac{1}{3}x - 4

**Answer:**

y = -\frac{1}{3}x - 4