Question

2 multiple choice 1 point
y = -3x + 6 and y = 6 - 3x
a. parallel b. intersecting c. same line (infinitely many)
○ a
○ b
○ c
clear my selection
3 multiple choice 1 point
y = 4/3x - 6 and y = 3/4 x + 6
a. parallel b. intersecting c. same line (infinitely many)
○ a
○ b
○ c
clear my selection

Explanation:

Step1: Analyze Question 2 equations

Rewrite both equations in slope-intercept form $y=mx+b$, where $m$ is slope, $b$ is y-intercept.
First equation: $y=-3x+6$, so $m_1=-3$, $b_1=6$
Second equation: $y=6-3x=-3x+6$, so $m_2=-3$, $b_2=6$
Since $m_1=m_2$ and $b_1=b_2$, the lines are identical.

Step2: Analyze Question 3 equations

Rewrite both equations in slope-intercept form $y=mx+b$.
First equation: $y=\frac{4}{3}x-6$, so $m_1=\frac{4}{3}$, $b_1=-6$
Second equation: $y=\frac{3}{4}x+6$, so $m_2=\frac{3}{4}$, $b_2=6$
Since $m_1
eq m_2$, the lines intersect at one point.

Answer:

1. Question 2: C. Same Line (Infinitely many)
2. Question 3: B. Intersecting