Question

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question
find the equation of a line perpendicular to $2x - 2y = 2$ that passes through the point $(-1,4)$.
answer attempt 1 out of 2
$\bigcirc y - 4 = -(x + 1)$
$\bigcirc y - 4 = x + 1$
$\bigcirc y + 4 = -(x - 1)$
$\bigcirc y + 4 = x - 1$

Explanation:

Step1: Find slope of given line

Rewrite $2x - 2y = 2$ to slope-intercept form $y=mx+b$:
$-2y = -2x + 2$
$y = x - 1$
Slope of given line $m_1=1$

Step2: Find perpendicular slope

Perpendicular slope $m_2 = -\frac{1}{m_1} = -1$

Step3: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$, where $(x_1,y_1)=(-1,4)$ and $m=-1$
$y - 4 = -1(x - (-1))$
Simplify: $y - 4 = -(x + 1)$

Answer:

$\boldsymbol{y - 4 = -(x + 1)}$ (Option 1)