Question

are these lines parallel, perpendicular, or neither? :
x + 2y = 3
y = 2x - 5
parallel
neither
perpendicular

Explanation:

Step1: Find slope of first line

Rewrite \(x + 2y = 3\) in slope - intercept form (\(y=mx + b\), where \(m\) is the slope).
Subtract \(x\) from both sides: \(2y=-x + 3\).
Divide by 2: \(y=-\frac{1}{2}x+\frac{3}{2}\). So slope \(m_1 =-\frac{1}{2}\).

Step2: Find slope of second line

The second line is \(y = 2x-5\), so its slope \(m_2 = 2\).

Step3: Check parallel/perpendicular

• Parallel lines have equal slopes (\(m_1=m_2\)). Here \(-\frac{1}{2}

eq2\), so not parallel.

• Perpendicular lines have slopes that are negative reciprocals (\(m_1\times m_2=- 1\)).

Calculate \(m_1\times m_2=-\frac{1}{2}\times2=-1\). So they are perpendicular.

Answer:

Perpendicular