Question

what do the following two equations represent?

• (y = 6x - 2)
• (2x - 12y = 24)

choose 1 answer:
a the same line
b distinct parallel lines
c perpendicular lines
d intersecting, but not perpendicular lines

Explanation:

Step1: Rewrite the second equation in slope - intercept form.

Starting with $2x−12y = 24$, we solve for $y$. First, subtract $2x$ from both sides: $-12y=-2x + 24$. Then divide by $-12$: $y=\frac{1}{6}x - 2$.

Step2: Identify the slopes of the two lines.

The first line $y = 6x-2$ has a slope $m_1 = 6$. The second line $y=\frac{1}{6}x - 2$ has a slope $m_2=\frac{1}{6}$.

Step3: Analyze the relationship between the slopes.

If two lines are parallel, their slopes are equal. Here $m_1
eq m_2$, so they are not parallel. If two lines are perpendicular, the product of their slopes is $- 1$. Since $m_1\times m_2=6\times\frac{1}{6}=1
eq - 1$, they are not perpendicular. So they are intersecting, but not perpendicular.

Answer:

D. Intersecting, but not perpendicular lines