# Find the coordinates of a point where a line intersects the y-axis.

• vparikh
In summary, the conversation discusses finding the coordinates of the point where a given line intersects the y-axis, using the equation of a line in 3D. After some discussion and attempted solutions, it is determined that the coordinates of the point are <0,2,0>.
vparikh

## Homework Statement

The following equation describes a straight line:
⟨x, y, z⟩ = ⟨−1, 0, −2⟩ + t⟨1, 2, 2⟩
Find the coordinates of the point where this line intersects the y-axis.

## Homework Equations

Equation of a Line: r = ro + tv

## The Attempt at a Solution

I'm not really sure how y-intercepts work in 3d and I'm having trouble even attempting a solution. My guess was the ro point <-1,0,-2> because the y coordinate is zero but I don't think that it would be that easy. Also, this is my first time posting a question on the Physics Forum site so please go easy on me if I messed anything up :)

vparikh said:

## Homework Statement

The following equation describes a straight line:
⟨x, y, z⟩ = ⟨−1, 0, −2⟩ + t⟨1, 2, 2⟩
Find the coordinates of the point where this line intersects the y-axis.

## Homework Equations

Equation of a Line: r = ro + tv

## The Attempt at a Solution

I'm not really sure how y-intercepts work in 3d and I'm having trouble even attempting a solution. My guess was the ro point <-1,0,-2> because the y coordinate is zero but I don't think that it would be that easy. Also, this is my first time posting a question on the Physics Forum site so please go easy on me if I messed anything up :)

It's almost that easy. <-1,0,-2> is in the x-z plane, it isn't on the y-axis. A point on the y-axis looks like <0,y,0>.

So then it has to be the point when the x and z coordinates are zero?

vparikh said:
So then it has to be the point when the x and z coordinates are zero?

Yes. What is it?

Well the equation multiplied out would be

<t-1,2t,2t-2>

so to make the x and z zero, x has to be 1 and y has to be 1.

So would <1,1,1> be a point that this line intersects the y axis?

vparikh said:
Well the equation multiplied out would be

<t-1,2t,2t-2>

so to make the x and z zero, x has to be 1 and y has to be 1.

So would <1,1,1> be a point that this line intersects the y axis?

Not quite sure what you are thinking there. I would say to put x=0 you should pick t=1.

Okay, so where t=1 the coordinates are <0,0,0> and thus intersect the y-axis at that point?

Wait, no it would be <0,2,0>

vparikh said:
Okay, so where t=1 the coordinates are <0,0,0> and thus intersect the y-axis at that point?

?Can you explain how putting t=1 into <t-1,2t,2t-2> gives you <0,0,0>?

Dick said:
?Can you explain how putting t=1 into <t-1,2t,2t-2> gives you <0,0,0>?

vparikh said:

Ok. Yes, it's <0,2,0>.

Dick said:
Ok. Yes, it's <0,2,0>.

Thanks for the help, I really appreciate it!

## 1. What does it mean to find the coordinates of a point where a line intersects the y-axis?

When a line intersects the y-axis, it means that the line crosses the vertical axis at a specific point. Finding the coordinates of this point means determining the value of the y-coordinate at the point where the line crosses the y-axis.

## 2. How do you find the coordinates of a point where a line intersects the y-axis?

To find the coordinates of a point where a line intersects the y-axis, you can use the slope-intercept form of a line (y = mx + b) and set x = 0. This will give you the value of b, which represents the y-intercept and therefore the y-coordinate of the point of intersection.

## 3. Can a line intersect the y-axis at more than one point?

No, a line can only intersect the y-axis at one point. This is because the y-axis is a vertical line and therefore only crosses the x-axis at one specific point.

## 4. What is the significance of finding the coordinates of a point where a line intersects the y-axis?

Finding the coordinates of a point where a line intersects the y-axis can help you better understand the behavior of the line. It can also help you determine the slope of the line, as well as the y-intercept, which is an important factor in graphing linear equations.

## 5. Are there any other methods for finding the coordinates of a point where a line intersects the y-axis?

Yes, there are other methods for finding the coordinates of a point where a line intersects the y-axis. One method is using the point-slope form of a line (y - y1 = m(x - x1)) and plugging in the coordinates of a point that lies on the line. Another method is graphing the line and visually determining the point of intersection with the y-axis.

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