Question

tina is designing a new street map for the city. she wants to ensure that main street and oak avenue cross each other at a right angle. if y = 2x + 1 represents main street on the map, which of the following equations can be used to represent oak avenue? a y = -2x + 1 b y = 2x + 3 c y = -1/2x + 14 d y = 1/2x - 7

Explanation:

Step1: Recall perpendicular - line slope rule

The slopes of two perpendicular lines are negative reciprocals of each other. The equation of Main Street is \(y = 2x+1\), and its slope \(m_1 = 2\).

Step2: Find the slope of Oak Avenue

The slope \(m_2\) of a line perpendicular to the line with slope \(m_1\) is \(m_2=-\frac{1}{m_1}\). Since \(m_1 = 2\), then \(m_2=-\frac{1}{2}\).

Step3: Check the options

We need to find the equation of the line with slope \(-\frac{1}{2}\). Option C: \(y =-\frac{1}{2}x + 14\) has a slope of \(-\frac{1}{2}\).

Answer:

C. \(y =-\frac{1}{2}x + 14\)