Question

which of the following linear functions has a graph that does not intersect with the function ( y = x + 3 )?
( y = 2x + 1 )
( y = 5x - 6 )
( y = x - 4 )
( y = 3x + 2 )

Explanation:

Step1: Recall parallel line rule

Linear functions with identical slopes ($m$) are parallel and do not intersect. The given function is $y = x + 3$, so its slope $m_1 = 1$.

Step2: Match slopes of options

Check the slope ($m$) of each option:

• $y=2x+1$: $m=2$
• $y=5x-6$: $m=5$
• $y=x-4$: $m=1$
• $y=3x+2$: $m=3$

Only $y=x-4$ has the same slope as $y=x+3$.

Answer:

$\boldsymbol{y = x - 4}$