Question

(04.02 mc)
randolph is creating rectangle wxyz so that wx has an equation of ( y = \frac{1}{4}x + 4 ). segment xy must pass through the point (-2, 6). which of the following is the equation for xy?
( y - 6 = \frac{1}{4}(x - (-2)) )
( y - (-2) = \frac{1}{4}(x - 6) )
( y - 6 = -4(x - (-2)) )
( y - (-2) = -4(x - 6) )

Explanation:

Step1: Find slope of XY

In a rectangle, adjacent sides are perpendicular. The slope of WX is $\frac{1}{4}$, so the slope of perpendicular XY is $m = -4$ (since perpendicular slopes multiply to -1: $\frac{1}{4} \times -4 = -1$).

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=-4$, $x_1=-2$, $y_1=6$.
$y - 6 = -4(x - (-2))$

Answer:

B. $y - 6 = -4(x - (-2))$