Question

question
find the equation of a line perpendicular to $y = -\frac{1}{2}x + 9$ that passes through the point $(1,7)$.
answer
$\circ \\ y + 7 = -\frac{1}{2}(x + 1)$
$\circ \\ y - 7 = \frac{1}{2}(x - 1)$
$\circ \\ y - 7 = 2(x - 1)$
$\circ \\ y - 7 = 2(x + 1)$
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Explanation:

Step1: Find perpendicular slope

The slope of $y = -\frac{1}{2}x + 9$ is $m_1 = -\frac{1}{2}$. Perpendicular slope $m_2 = 2$ (since $m_1 \times m_2 = -1$).

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $(x_1,y_1)=(1,7)$ and $m=2$.
$y - 7 = 2(x - 1)$

Answer:

$\boldsymbol{y - 7 = 2(x - 1)}$