Question

1. match the lines with their orientation:

draggable item \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\tcorresponding item
$y = -\frac{1}{3}x - 2$ \t\t\t\t\t\t\t\t\t\t→ \t\t\tparallel to $y = 3x + 1$
$y = 2x - 4$ \t\t\t\t\t\t\t\t\t\t→ \t\t\tperpendicular to $y = 3x + 1$
$y = 3x$ \t\t\t\t\t\t\t\t\t\t→ \t\t\tparallel to $y = 2x + 3$

Explanation:

Step1: Recall parallel line rule

Parallel lines have equal slopes ($m_1=m_2$)

Step2: Recall perpendicular line rule

Perpendicular lines have slopes that are negative reciprocals: $m_1=-\frac{1}{m_2}$

Step3: Analyze $y=-\frac{1}{3}x+2$

Slope $m=-\frac{1}{3}$. For $y=3x+1$, $m=3$, and $-\frac{1}{3}=-\frac{1}{3}$, so it is perpendicular to $y=3x+1$.

Step4: Analyze $y=2x-4$

Slope $m=2$. For $y=2x+3$, $m=2$, so it is parallel to $y=2x+3$.

Step5: Analyze $y=3x$

Slope $m=3$. For $y=3x+1$, $m=3$, so it is parallel to $y=3x+1$.

Answer:

• $y = -\frac{1}{3}x + 2$ → Perpendicular to $y=3x+1$
• $y = 2x - 4$ → Parallel to $y=2x+3$
• $y = 3x$ → Parallel to $y=3x+1$