Question

question
what is an equation of the line that passes through the point (2, 8) and is perpendicular to the line x - y = 4?
answer

Explanation:

Step1: Find slope of given line

Rewrite $x - y = 4$ as $y = x - 4$. Slope $m_1 = 1$.

Step2: Find slope of perpendicular line

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

Step3: Use point-slope form

Point $(2,6)$, formula: $y - y_1 = m_2(x - x_1)$
$y - 6 = -1(x - 2)$

Step4: Simplify to slope-intercept form

$y - 6 = -x + 2$
$y = -x + 8$
Or standard form: $x + y = 8$

Answer:

$y = -x + 8$ (or $x + y = 8$)