Question

question 6 (multiple choice worth 1 points) (04.02r mc) the equation of line qr is $x + 2y = 2$. what is the equation of a line perpendicular to line qr in slope-intercept form that contains point $(5, 6)$?
$y = -\frac{1}{2}x + \frac{17}{2}$
$y = 2x - 4$
$y = -\frac{1}{2}x + \frac{7}{2}$
$y = 2x + 16$

Explanation:

Step1: Find slope of line QR

Rewrite $x + 2y = 2$ to slope-intercept form $y=mx+b$:
$2y = -x + 2$
$y = -\frac{1}{2}x + 1$
Slope of QR: $m_1 = -\frac{1}{2}$

Step2: Find perpendicular slope

Perpendicular slopes multiply to $-1$:
$m_2 = \frac{-1}{m_1} = \frac{-1}{-\frac{1}{2}} = 2$

Step3: Find y-intercept of new line

Use point $(5,6)$ and $y=mx+b$:
$6 = 2(5) + b$
$6 = 10 + b$
$b = 6 - 10 = -4$

Step4: Write final equation

Combine slope and y-intercept:
$y = 2x - 4$

Answer:

B. $y = 2x - 4$