Question

what is the equation of the line that passes through the point (6, -4) and has a slope of $-\frac{1}{3}$?

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)=(6, -4)$ and $m=-\frac{1}{3}$.
Substitute values: $y - (-4) = -\frac{1}{3}(x - 6)$

Step2: Simplify the equation

Simplify the left side: $y + 4 = -\frac{1}{3}(x - 6)$
Distribute the slope: $y + 4 = -\frac{1}{3}x + 2$

Step3: Isolate y to get slope-intercept form

Subtract 4 from both sides: $y = -\frac{1}{3}x + 2 - 4$
Combine constants: $y = -\frac{1}{3}x - 2$

Answer:

$y = -\frac{1}{3}x - 2$ (or in standard form: $x + 3y = -6$)