Question

question 2 multiple - choice worth 4 points
randolph is creating rectangle wxyz so that wx has an equation of y = 1/4x + 4. segment xy must pass through the point (-2, 6). which of the following is the equation for xy?
y - 6 = - 4(x - (-2))
y - 6 = 1/4(x - (-2))
y - (-2) = 1/4(x - 6)
y - (-2) = - 4(x - 6)

Explanation:

Step1: Recall slope - perpendicular relationship

In a rectangle, adjacent sides are perpendicular. If the slope of line WX is $m_1=\frac{1}{4}$, the slope of line XY (perpendicular to WX) is $m_2=- 4$ (since the product of slopes of two perpendicular lines is - 1, i.e., $m_1\times m_2=-1$, so $\frac{1}{4}\times m_2=-1$ gives $m_2 = - 4$).

Step2: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-2,6)$ and $m=-4$. Substitute these values into the formula:
$y - 6=-4(x+2)$

Answer:

$y - 6=-4(x + 2)$