Question

line 1: y = x - 4 line 2: y = x + 9 are the lines shown parallel, perpendicular, neither or the same line? the same line parallel neither parallel nor perpendicular perpendicular

Explanation:

Step1: Identify the slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For line 1: $y=x - 4$, the slope $m_1=1$. For line 2: $y=x + 9$, the slope $m_2=1$.

Step2: Apply parallel and perpendicular rules

Two lines are parallel if $m_1=m_2$, perpendicular if $m_1\times m_2=- 1$. Since $m_1 = 1$ and $m_2 = 1$, $m_1=m_2$, and $m_1\times m_2=1\times1 = 1
eq - 1$. Also, the y - intercepts ($-4$ and $9$) are different, so they are not the same line.

Answer:

parallel