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Chapter 3: Problem 53

Find an equation of the line that satisfies the given conditions. Through \((0.5,0.2) ;\) vertical

Short Answer

Expert verified
The equation is \(x = 0.5\).

Step by step solution

01

Identify Line Characteristics

A vertical line has an undefined slope and passes through all points with the same x-coordinate.
02

Determine the x-coordinate

For a vertical line passing through \(0.5, 0.2\), the x-coordinate is constant at \(0.5\).
03

Write the Equation

Since the x-coordinate remains \(0.5\), the equation of the line is written as \(x = 0.5\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Vertical Line
A vertical line is a special type of line in geometry and algebra. It runs straight up and down and does not tilt in any way. Every point on a vertical line has the same x-coordinate.

For example, consider the vertical line going through the point (0.5, 0.2). No matter which point you choose on that line, the x-coordinate will always be 0.5. This is a key characteristic of vertical lines. They do not follow the y = mx + b form of a standard linear equation because they do not have a slope like non-vertical lines.
Undefined Slope
The concept of slope refers to the steepness or incline of a line. For most lines, this is measured as 'rise over run,' or the change in the y-coordinates divided by the change in the x-coordinates.

However, vertical lines are an exception. Because the x-coordinates of a vertical line do not change, the 'run' part of the slope calculation becomes zero. Dividing by zero is mathematically impossible, which gives us an undefined slope for vertical lines. So, when you see or need to describe a vertical line, remember that its slope is undefined.
x-coordinate
In any point (x, y), the x-coordinate is its horizontal position. For a vertical line, this x-coordinate remains constant.

In our given problem, we have a vertical line passing through the point \(0.5, 0.2\). Therefore, the x-coordinate of every point on this line is 0.5. Since vertical lines do not change along the x-axis, their equation is simple and straightforward. Simply write the equation as x = constant value. For our specific problem, the equation becomes \ x = 0.5 \.

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Most popular questions from this chapter

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