Question

what is an equation of the line that passes through the point (4, 8) and is perpendicular to the line ( x + 2y = 12 )?
answer
input box submit answer button

Explanation:

Step1: Find slope of given line

Rewrite $x + 2y = 12$ in slope-intercept form $y=mx+b$:
$2y = -x + 12$
$y = -\frac{1}{2}x + 6$
Slope of given line: $m_1 = -\frac{1}{2}$

Step2: Find perpendicular slope

Perpendicular slopes are negative reciprocals:
$m_2 = -\frac{1}{m_1} = -\frac{1}{-\frac{1}{2}} = 2$

Step3: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$ with $(x_1,y_1)=(4,8)$ and $m=2$:
$y - 8 = 2(x - 4)$

Step4: Simplify to slope-intercept form

Expand and rearrange:
$y - 8 = 2x - 8$
$y = 2x$

Answer:

$y = 2x$ (or equivalent forms like $2x - y = 0$)