Question

a rectangle is graphed on the coordinate grid. which equation represents a side that is perpendicular to side d?
○ ( y = 2x + 5 )
○ ( y = -2x + 5 )

Explanation:

Step1: Find slope of side d

Side d connects \((-4, 3)\) and \((0, 5)\). Slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
\(m_d = \frac{5 - 3}{0 - (-4)} = \frac{2}{4} = \frac{1}{2}\).

Step2: Find slope of perpendicular line

Perpendicular slopes multiply to \(-1\). Let \(m\) be slope of perpendicular line.
\(\frac{1}{2} \times m = -1 \implies m = -2\).

Step3: Identify equation with slope -2

Check options:

• \(y = 2x + 5\) has slope \(2\).
• \(y = -2x + 5\) has slope \(-2\).

Answer:

\(y = -2x + 5\)