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Chapter 7: Problem 62

Write an equation of the line passing through the given point and satisfying the given condition. (-4,-2)\(;\) slope 0

Short Answer

Expert verified
The equation of the line is ewline y = -2.

Step by step solution

01

Identify the Point and Slope

The given point is ewline (-4, -2) and the given slope is 0.
02

Understand the Slope

A slope of 0 indicates a horizontal line. This means the y-coordinate remains the same for all values of x.
03

Write the Equation of the Horizontal Line

For a horizontal line passing through (-4, -2), the equation will be: ewline y = -2. ewline The y-coordinate of the point is -2 and since it's a horizontal line, y will always remain -2.

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Key Concepts

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

Identifying Points
In the context of graphing equations, a point is represented as \((x, y)\). The given point \((-4, -2)\) tells us the line passes through the coordinates where x is -4 and y is -2.
It's important to identify these coordinates correctly because they help in forming the equation of the line. Always remember, in an ordered pair like \((x, y)\), the first value represents the x-coordinate, and the second value represents the y-coordinate. For example, in \((-4, -2)\), -4 is the x-coordinate, and -2 is the y-coordinate.
Correctly identifying points is the first step in determining the equation of the line they describe.
Slope of a Line
The slope of a line defines its steepness or angle and is represented by the letter \(m\). It's calculated as the change in y divided by the change in x, which is expressed mathematically as:
\[ m = \frac{\Delta y}{\Delta x} \]
A slope of 0 indicates a horizontal line. This means that the y-coordinate remains constant regardless of the x-coordinate. Horizontal lines run parallel to the x-axis and do not incline or decline.
For example, if a line has a slope of 0 and passes through any point \((x, -2)\), the value of y will always be -2, and the line will be perfectly horizontal.
Horizontal Line Equation
When a line is horizontal, its equation takes a simple form. Since the slope \(m\) is 0, it means there is no vertical change no matter how much we move horizontally. The equation of a horizontal line passing through any point \((x, -2)\) will always be:
\[ y = -2 \]
This equation tells us that for every value of x, the value of y will always be -2, forming a straight, horizontal line. Unlike other linear equations that have the form \(y = mx + b\), horizontal line equations do not include x because the slope does not change.
In our specific case, for the line passing through the point \((-4, -2)\) with a slope of 0, the equation is simply:
\[ y = -2 \]

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