Question

the equations of three lines are given below.
line 1: $y=-4x+8$
line 2: $8x+2y=4$
line 3: $y=4x-3$
for each pair of lines, determine whether they are parallel, perpendicular, or neither.
line 1 and line 2: $circ$ parallel $circ$ perpendicular $circ$ neither
line 1 and line 3: $circ$ parallel $circ$ perpendicular $circ$ neither
line 2 and line 3: $circ$ parallel $circ$ perpendicular $circ$ neither

Explanation:

Step1: Convert Line2 to slope-intercept form

Rearrange $8x+2y=4$ to $y=mx+b$:
$2y=-8x+4$
$y=-4x+2$

Step2: Identify slopes of all lines

• Line1 slope: $m_1=-4$
• Line2 slope: $m_2=-4$
• Line3 slope: $m_3=4$

Step3: Compare Line1 & Line2 slopes

Parallel lines have equal slopes: $m_1=m_2=-4$

Step4: Compare Line1 & Line3 slopes

Check perpendicularity: $m_1 \times m_3 = (-4)(4) = -16
eq -1$; slopes not equal.

Step5: Compare Line2 & Line3 slopes

Check perpendicularity: $m_2 \times m_3 = (-4)(4) = -16
eq -1$; slopes not equal.

Answer:

Line 1 and Line 2: Parallel
Line 1 and Line 3: Neither
Line 2 and Line 3: Neither