Equation of a Line Passing Through (-3, 4) and Parallel to the Y-Axis

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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. Participants explore how to express this line in the forms y = mx + b and Ax + By + C = 0, addressing the challenges associated with these representations.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that the line is represented by the equation x = -3.
  • Others argue that it is impossible to express the line in the form y = mx + b, as this form implies a function where each x corresponds to a single y, which does not apply here.
  • There is a discussion about expressing the line in the form Ax + By + C = 0, with participants suggesting various representations such as 3x + 0B + C = 0 and x + 0y + 3 = 0.
  • One participant introduces a general form by letting x = -a, leading to the equations x + a = 0 and x + 0y + a = 0.

Areas of Agreement / Disagreement

Participants generally agree on the equation of the line being x = -3, but there is disagreement on how to express this line in the requested forms, particularly y = mx + b, which remains unresolved.

Contextual Notes

Participants note that the equation y = mx + b is not applicable for vertical lines, which complicates the discussion on how to represent the line in standard forms.

Who May Find This Useful

This discussion may be useful for students learning about linear equations, particularly those exploring the characteristics of vertical lines and their representations in different mathematical forms.

mathdad
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Find an equation of the line passing through (-3, 4) and
parallel to the y-axis. Express final answer in the forms
y = mx + b and Ax + By + C = 0.

I think the line has got to be x = -3.

How do I write the final answer in the two requested forms given above?
 
Last edited:
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RTCNTC said:
Find an equation of the line passing through (-3, 4) and
parallel to the y-axis. Express final answer in the forms
y = mx + b and Ax + By + C = 0.

I am think that the line has got to be x = -3.
Yes.

RTCNTC said:
How do I write the final answer in the two requested forms given above?
It's impossible to express this equation in the form y = mx + b. This form represents a function y(x), and the line in question is not the graph of any function y(x) because one x corresponds to all possible y's rather than just one y. Concerning the form Ax + By + C = 0, I don't see the difficulty. (You have not forgotten how to move terms from one side of an equation to the other, have you?) Keep in mind that some of A, B and C can be zeros. The only restriction for it to be the equation of a line is that both A and B should not be zeros simultaneously.
 
Ok. For x = -3, I got the following general equation of a line:

3x + 0B + C = 0

Correct?
 
RTCNTC said:
Ok. For x = -3, I got the following general equation of a line:

3x + 0B + C = 0

Correct?

Let's begin with:

$$x=-3$$

To write this in the form Ax + By + C = 0, we want the RHS to be 0, so add 3 to both sides:

$$x+3=0$$

Since there is no "y" term on the LHS, we may add 0y to it:

$$x+0y+3=0$$

or:

$$1x+0y+3=0$$

We see then that:

$$(A,B,C)=(1,0,3)$$
 
Let x = -a

Then in general we can write it as x + a = 0.

We can also write x + 0y + a = 0 or 1x + 0y + a = 0.

Correct?
 
RTCNTC said:
Let x = -a

Then in general we can write it as x + a = 0.

We can also write x + 0y + a = 0 or 1x + 0y + a = 0.

Correct?

Yes, indeed. :D
 
I am not close to where most tutors are in terms of math in this website but I definitely have learned a lot.
 

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