Question

what do the following two equations represent?

• $5x + y = 3$
• $10x + 2y = -6$

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

Explanation:

Step1: Convert to slope - intercept form

For the first equation \(5x + y=3\), solve for \(y\):
\(y=- 5x + 3\). The slope \(m_1=-5\) and the y - intercept \(b_1 = 3\).

For the second equation \(10x+2y=-6\), divide the entire equation by 2: \(5x + y=-3\), then solve for \(y\): \(y=-5x-3\). The slope \(m_2=-5\) and the y - intercept \(b_2=-3\).

Step2: Analyze the slopes and intercepts

Since the slopes \(m_1 = m_2=-5\) (so the lines are parallel) and the y - intercepts \(b_1
eq b_2\) ( \(3
eq - 3\) ), the two lines are distinct parallel lines.

Answer:

B. Distinct parallel lines