Question

3y = 4x + 3 and 3x + 4y = 9

1. identify whether the lines are parallel, perpendicular, or neither.

perpendicular
parallel
neither

Explanation:

Step1: Find slope of first line

Given \(3y = 4x + 3\), divide by 3: \(y=\frac{4}{3}x + 1\). Slope \(m_1=\frac{4}{3}\).

Step2: Find slope of second line

Given \(3x + 4y = 9\), solve for \(y\): \(4y=-3x + 9\), \(y=-\frac{3}{4}x+\frac{9}{4}\). Slope \(m_2 = -\frac{3}{4}\).

Step3: Check product of slopes

Multiply \(m_1\) and \(m_2\): \(\frac{4}{3}\times(-\frac{3}{4})=-1\). When product is -1, lines are perpendicular.

Answer:

perpendicular