Question

1. a.gsr.3.1: the sidewalks on both sides of peach st. are parallel. one sidewalk can be modeled by the equation 2x - y = -1 which equation could model the other sidewalk? a. 2x + y = 8 b. $y = \frac{1}{2}x + 3$ c. y - 1 = 2(x - 3) d. y = -2x - 1

Explanation:

Step1: Find slope of given line

Rewrite \(2x - y = -1\) in slope - intercept form (\(y=mx + b\), where \(m\) is the slope).
\(2x - y=-1\) can be rewritten as \(y = 2x+ 1\). So the slope (\(m_1\)) of the given line is \(2\).

Step2: Recall slope of parallel lines

Parallel lines have equal slopes. So the equation of the other sidewalk (parallel line) must have a slope of \(2\).

Step3: Analyze each option

• Option A: Rewrite \(2x + y=8\) as \(y=-2x + 8\). The slope is \(- 2\), not equal to \(2\).
• Option B: The equation \(y=\frac{1}{2}x + 3\) has a slope of \(\frac{1}{2}\), not equal to \(2\).
• Option C: Rewrite \(y - 1=2(x - 3)\) using the distributive property: \(y-1 = 2x-6\), then \(y=2x-5\). The slope is \(2\), which is equal to the slope of the given line.
• Option D: The equation \(y=-2x - 1\) has a slope of \(-2\), not equal to \(2\).

Answer:

C. \(y - 1 = 2(x - 3)\)