A Parallel Line Passing Through (-3, 4)

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Discussion Overview

The discussion revolves around finding the equation of a line that passes through the point (-3, 4) and is parallel to the y-axis. The focus is on understanding the properties of vertical lines and their equations.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Some participants assert that a line parallel to the y-axis must also be a vertical line.
  • It is proposed that vertical lines can be expressed in the form x = k, where k is the x-coordinate of any point on the line.
  • Participants discuss the specific x-coordinate of the point (-3, 4) and confirm it is -3.
  • There is a suggestion that the equation of the line in question is x = -3, based on the x-coordinate of the given point.
  • One participant explains that for vertical lines, the x-coordinate remains constant regardless of the y-coordinate.
  • Another participant agrees that the line x = -3 is parallel to the line x = 0.

Areas of Agreement / Disagreement

Participants generally agree on the properties of vertical lines and the conclusion that the line passing through (-3, 4) is x = -3. However, the discussion does not explore any alternative interpretations or models.

Contextual Notes

The discussion assumes familiarity with the concept of vertical lines and their equations, but does not delve into any potential exceptions or broader contexts.

Who May Find This Useful

This discussion may be useful for students learning about the properties of lines in coordinate geometry, particularly those focusing on vertical lines and their equations.

mathdad
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Find an equation of the line that passes through (-3, 4) and is parallel to the y-axis.

The y-axis is the line x = 0.

The equation that passes through the given point must also be a vertical line because it is parallel to the line
x = 0 or the y-axis.

Correct?

Can someone provide a useful hint?
 
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RTCNTC said:
Find an equation of the line that passes through (-3, 4) and is parallel to the y-axis.

The y-axis is the line x = 0.

The equation that passes through the given point must also be a vertical line because it is parallel to the line
x = 0 or the y-axis.

Correct?

Can someone provide a useful hint?

A vertical line can be written in the form:

$$x=k$$

where $k$ (a real constant) is the $x$-coordinate of every point on the line. :)
 
MarkFL said:
A vertical line can be written in the form:

$$x=k$$

where $k$ (a real constant) is the $x$-coordinate of every point on the line. :)

Give me a second hint.
 
RTCNTC said:
Give me a second hint.

What is the $x$-coordinate of the given point?
 
MarkFL said:
What is the $x$-coordinate of the given point?

The x-coordinate of the given point is -3.

Is the line x = -3?
 
RTCNTC said:
The x-coordinate of the given point is -3.

Is the line x = -3?

Yes, for any given vertical line, no matter what the $y$-coordinate of a particular point on that line, the $x$-coordinate will be the same throughout. The locus of all points having the same $x$-coordinate is a vertical line. :)
 
MarkFL said:
Yes, for any given vertical line, no matter what the $y$-coordinate of a particular point on that line, the $x$-coordinate will be the same throughout. The locus of all points having the same $x$-coordinate is a vertical line. :)

This makes sense. The line x = -3 is // to the line x = 0.
 

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