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

[mathdad]

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?

 

[Evgeny.Makarov]

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.

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.

 

[mathdad]

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

3x + 0B + C = 0

Correct?

 

[MarkFL]

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:

$$(A,B,C)=(1,0,3)$$

 

[mathdad]

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?

 

[MarkFL]

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

 

[mathdad]

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