MHB A Parallel Line Passing Through (-3, 4)

[mathdad]

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?

 

[MarkFL]

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. :)

 

[mathdad]

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.

 

[MarkFL]

Give me a second hint.

What is the $x$-coordinate of the given point?

 

[mathdad]

What is the $x$-coordinate of the given point?

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

Is the line x = -3?

 

[MarkFL]

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. :)

 

[mathdad]

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.