Question

5-104. write the equation of the line parallel to $y = -\frac{1}{3}x + 5$ passing through the point (9, -1).

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. The given line is $y = -\frac{1}{3}x + 5$, so the slope $m = -\frac{1}{3}$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m = -\frac{1}{3}$, $x_1=9$, $y_1=-1$.
$y - (-1) = -\frac{1}{3}(x - 9)$

Step3: Simplify to slope-intercept form

Simplify the left side: $y + 1 = -\frac{1}{3}(x - 9)$
Distribute the slope: $y + 1 = -\frac{1}{3}x + 3$
Subtract 1 from both sides: $y = -\frac{1}{3}x + 2$

Answer:

$y = -\frac{1}{3}x + 2$