Question

warm-up a given line has the following equation: ( y = 3x - 5 ) drag each equation to the correct location beneath the descriptions. not all equations will be used. same as given line parallel to given line perpendicular to given line equations: ( 3x + y = 15 ), ( x + 3y = -15 ), ( 3x - y = 5 ), ( 3x + y = -5 ), ( 3x - y = -5 )

Explanation:

Step1: Find slope of given line

The given line is $y=3x-5$, so its slope $m_1=3$.

Step2: Rewrite equations to slope-intercept form

For each equation, solve for $y$ to find slope:

1. $3x+y=15$ → $y=-3x+15$, slope $m=-3$
2. $x+3y=-15$ → $y=-\frac{1}{3}x-5$, slope $m=-\frac{1}{3}$
3. $3x-y=5$ → $y=3x-5$, slope $m=3$
4. $3x+y=-5$ → $y=-3x-5$, slope $m=-3$
5. $3x-y=-5$ → $y=3x+5$, slope $m=3$

Step3: Classify by slope rules

• Same line: Slope and intercept match given line.
• Parallel: Slopes are equal ($m=3$).
• Perpendicular: Slopes are negative reciprocals ($m_1 \times m_2 = -1$, so $m=-\frac{1}{3}$).

Answer:

same as given line

$3x - y = 5$

parallel to given line

$3x - y = -5$

perpendicular to given line

$x + 3y = -15$