Question

what do the following two equations represent?

• (y + 6=-\frac{1}{3}(x - 15))
• (2x + 6y = 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 first equation in slope - intercept form

Starting with $y + 6=-\frac{1}{3}(x - 15)$. First, distribute the $-\frac{1}{3}$:
$y+6=-\frac{1}{3}x + 5$. Then subtract 6 from both sides:
$y=-\frac{1}{3}x-1$.

Step2: Rewrite the second equation in slope - intercept form

Starting with $2x + 6y=24$. First, isolate $y$:
$6y=-2x + 24$. Then divide each term by 6:
$y=-\frac{1}{3}x + 4$.

Step3: Analyze the slopes and y - intercepts

The slope of the first line is $m_1=-\frac{1}{3}$ and its y - intercept is $b_1=-1$.
The slope of the second line is $m_2=-\frac{1}{3}$ and its y - intercept is $b_2 = 4$.
Since the slopes are equal ($m_1=m_2=-\frac{1}{3}$) and the y - intercepts are different ($b_1
eq b_2$), the lines are distinct parallel lines.

Answer:

B. Distinct parallel lines