Question

determine if the lines are parallel (∥), perpendicular (⊥), or neither. (circle your answer)
5.
y = \frac{5}{3}x - 4
y = \frac{3}{5}x + 5
m₁ = ____
m₂ = ____
∥ ⊥ neither
(neither is circled)
6.
y = 3x - 7
y = 3x + 1
m₁ = ____
m₂ = ____
∥ ⊥ neither
8.
y = \frac{3}{2}x - 4
y - 1 = -\frac{2}{3}x + 4
m₁ = ____
m₂ = ____
∥ ⊥ neither
9.
y = -5x + 1
y + 4 = 5(x - 6)
m₁ = ____
m₂ = ____
∥ ⊥ neither
10.
y = x - 1
y - 2 = x + 1
m₁ = ____
m₂ = ____
∥ ⊥ neither

Explanation:

Problem 5

Step1: Identify slope of line 1

Line 1: $y=\frac{5}{3}x-4$, so $m_1=\frac{5}{3}$

Step2: Identify slope of line 2

Line 2: $y=\frac{3}{5}x+5$, so $m_2=\frac{3}{5}$

Step3: Check parallel/perpendicular

Parallel: $m_1=m_2$? $\frac{5}{3}
eq\frac{3}{5}$. Perpendicular: $m_1 \cdot m_2=-1$? $\frac{5}{3} \cdot \frac{3}{5}=1
eq-1$. So neither.

Problem 6

Step1: Identify slope of line 1

Line 1: $y=3x-7$, so $m_1=3$

Step2: Identify slope of line 2

Line 2: $y=3x+1$, so $m_2=3$

Step3: Check parallel/perpendicular

$m_1=m_2$, so lines are parallel.

Problem 7

Step1: Identify slope of line 1

Line 1: $y=\frac{1}{2}x-2$, so $m_1=\frac{1}{2}$

Step2: Identify slope of line 2

Line 2: $y=-2x+6$, so $m_2=-2$

Step3: Check parallel/perpendicular

$m_1 \cdot m_2=\frac{1}{2} \cdot (-2)=-1$, so lines are perpendicular.

Problem 8

Step1: Identify slope of line 1

Line 1: $y=\frac{3}{2}x-4$, so $m_1=\frac{3}{2}$

Step2: Rewrite line 2 to slope-intercept

$y-1=-\frac{2}{3}x+4 \implies y=-\frac{2}{3}x+5$, so $m_2=-\frac{2}{3}$

Step3: Check parallel/perpendicular

$m_1 \cdot m_2=\frac{3}{2} \cdot (-\frac{2}{3})=-1$, so lines are perpendicular.

Problem 9

Step1: Identify slope of line 1

Line 1: $y=-5x+1$, so $m_1=-5$

Step2: Rewrite line 2 to slope-intercept

$y+4=5(x-6) \implies y=5x-30-4 \implies y=5x-34$, so $m_2=5$

Step3: Check parallel/perpendicular

Parallel: $-5
eq5$. Perpendicular: $-5 \cdot 5=-25
eq-1$. So neither.

Problem 10

Step1: Identify slope of line 1

Line 1: $y=x-1$, so $m_1=1$

Step2: Rewrite line 2 to slope-intercept

$y-2=x+1 \implies y=x+3$, so $m_2=1$

Step3: Check parallel/perpendicular

$m_1=m_2$, so lines are parallel.

Answer:

1. $m_1=\frac{5}{3}$, $m_2=\frac{3}{5}$, neither
2. $m_1=3$, $m_2=3$, $\parallel$
3. $m_1=\frac{1}{2}$, $m_2=-2$, $\perp$
4. $m_1=\frac{3}{2}$, $m_2=-\frac{2}{3}$, $\perp$
5. $m_1=-5$, $m_2=5$, neither
6. $m_1=1$, $m_2=1$, $\parallel$