Question

question
find the equation of a line perpendicular to $y = -3x - 5$ that passes through the point $(9, 3)$.
answer
$\circ$ $y = -3x - 5$ $\circ$ $y = 3x - 5$
$\circ$ $y = -\frac{1}{3}x$ $\circ$ $y = \frac{1}{3}x$

Explanation:

Step1: Find perpendicular slope

The slope of $y=-3x-5$ is $m_1=-3$. Perpendicular slope $m_2 = \frac{1}{3}$ (since $m_1 \times m_2 = -1$).

Step2: Use point-slope form

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

Step3: Simplify to slope-intercept

Expand and isolate $y$:
$y - 3 = \frac{1}{3}x - 3$
$y = \frac{1}{3}x$

Answer:

$\boldsymbol{y = \frac{1}{3}x}$ (corresponding to the option $y = \frac{1}{3}x$)