Question

1. select all lines perpendicular to $y = -x + 3$:

$y = x - 1$
$y = \frac{1}{3}x + 3$
$y = 3x + 2$
$y = x$

Explanation:

Step1: Identify slope of given line

The line $y = -x + 3$ is in slope-intercept form $y=mx+b$, so its slope $m_1 = -1$.

Step2: Find required perpendicular slope

Perpendicular slopes multiply to $-1$. Let $m_2$ be the perpendicular slope:
$$m_1 \times m_2 = -1$$
$$-1 \times m_2 = -1 \implies m_2 = 1$$

Step3: Match slopes of options

Check which options have slope $m=1$:

• $y = x - 1$: slope $=1$
• $y = \frac{1}{3}x + 3$: slope $=\frac{1}{3}$
• $y = 3x + 2$: slope $=3$
• $y = x$: slope $=1$

Answer:

A. $y = x - 1$
D. $y = x$