Equations Of Vertical And Horizontal Lines

Equations Of Vertical And Horizontal Lineswrite

Write equations for the horizontal and vertical lines described in the real-world situations below.

1. In many cities and towns across the United States, the numbering system of the roads is based on a grid, similar to the latitude and longitude lines on a globe. Suppose the green lines in the following graph represent two east-west and two north-south running roads in a Midwestern town.

Write equations for the two horizontal and two vertical lines that represent roads in the town.

2. The Willis Tower (formerly known as the Sears Tower) in Chicago, Illinois, is the tallest building in the United States. Measuring 1,450 feet, the tower contains 110 stories filled with a combination of office and retail space. The base of the tower is made up of nine 75’ by 75’ squares.

Suppose the square graphed on the coordinate plane below represents the base of the Willis Tower. Write equations for the two horizontal and two vertical lines that pass through the square.

3. Think of another real-world situation that might involve horizontal and vertical lines. Write a description of the situation and draw the graph of a coordinate plane with two horizontal and two vertical lines to represent your situation.

Draw the lines so that two of them pass through positive values and the other two pass through negative values on the coordinate plane. Then write equations for all four of the lines on your graph.

Paper For Above instruction

In this paper, I will discuss the equations of horizontal and vertical lines based on the given real-world scenarios and develop mathematical models for each case. The purpose is to understand how to translate real-world spatial and structural situations into algebraic equations of lines, which can serve as a basis for analyzing and solving related problems.

1. Road Grid in a Midwestern Town

In many U.S. towns and cities, the road network follows a grid pattern where roads run east-west and north-south, resembling a coordinate plane. Suppose the town has two principal east-west roads and two principal north-south roads represented in the graph with green lines.

Assuming these roads are aligned with the grid, their equations are straightforward. Horizontal roads run parallel to the x-axis, meaning their equations are of the form y = constant. Vertical roads run parallel to the y-axis, with equations of the form x = constant.

For example, if the two east-west roads are at y = 2 and y = 5, then their equations are simply y = 2 and y = 5. Similarly, if the two north-south roads are at x = -3 and x = 4, their equations are x = -3 and x = 4. These equations define the roads in the town and help in understanding the city's layout.

2. Willis Tower Base in Chicago

The Willis Tower, with its base formed by a square measuring nine 75-foot by 75-foot sections, can be represented on a coordinate plane by placing the square in a convenient position. Suppose the square is positioned with its lower-left corner at the origin, (0, 0). Then, since each side measures 75 feet, the other corners will be at (75, 0), (75, 75), and (0, 75).

The equations of the lines passing through the square are based on these coordinates. The two horizontal lines are y = 0 and y = 75, representing the bottom and top edges of the base. The two vertical lines are x = 0 and x = 75, representing the left and right edges of the base.

If the square were located elsewhere,, say with its bottom-left corner at (x, y), the equations would shift accordingly as x = x0 and y = y0.

3. Example of a Different Real-World Situation

Consider a city park that has a rectangular pond with pathways crossing over it. Suppose the pond is centered at the origin, with pathways crossing through the middle. Two pathways run east-west, represented by the lines y = 2 and y = -3, while two run north-south, represented by x = -4 and x = 3. The paths pass through both positive and negative coordinates, creating a crossing grid.

This setup models the intersections and pathways in the park, which are important for navigation and planning. The equations are straightforward, with the horizontal paths at fixed y-values and vertical paths at fixed x-values, illustrating how lines can represent physical structures in a landscape.

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