General question about parameterized equations for lines

In summary, a parameterized equation for a line is a way to represent a line using two equations, one for the x-coordinate and one for the y-coordinate, with a parameter representing a point on the line. The slope and y-intercept can be determined by rearranging the equations, and the equation can represent both vertical and horizontal lines. A parameterized equation is not unique, but all equations representing the same line will have the same slope and y-intercept. To find a specific point on the line, a value can be substituted for the parameter in the equations.
  • #1
inknit
58
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I'm supposed to find the equation of a line perpendicular to and intersecting another line. The original line was parameterized in t.

I got the answer as L = (0, 1, 2) + s <3/2, -1/2, -1>


The book gave it as L = (0, 1 ,2> + t <3, -1, -2>



Since both equations describe the same line, is my answer okay?

Thanks!
 
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  • #2
hi inknit! :smile:
inknit said:
Since both equations describe the same line, is my answer okay?

yeees …

but theirs is obviously better :wink:
 

1. What is a parameterized equation for a line?

A parameterized equation for a line is a way to represent a line in the form of two equations, one for the x-coordinate and one for the y-coordinate, using a parameter (typically denoted as t or s) to represent a point on the line. This allows for a more flexible and general representation of a line compared to the standard slope-intercept form.

2. How do I determine the slope and y-intercept from a parameterized equation for a line?

To determine the slope and y-intercept from a parameterized equation for a line, you can rearrange the equations to solve for y in terms of x and the parameter. The coefficient of x will be the slope, and the constant term will be the y-intercept.

3. Can a parameterized equation for a line be used to represent vertical or horizontal lines?

Yes, a parameterized equation for a line can represent both vertical and horizontal lines. For a vertical line, the x-coordinate equation will have a constant value and the y-coordinate equation will have the parameter. For a horizontal line, the x-coordinate equation will have the parameter and the y-coordinate equation will have a constant value.

4. Is a parameterized equation for a line unique?

No, a parameterized equation for a line is not unique. There are infinitely many parameterized equations that can represent the same line. However, they will all have the same slope and y-intercept.

5. How can I use a parameterized equation for a line to find a specific point on the line?

To find a specific point on a line represented by a parameterized equation, you can substitute a value for the parameter into the equations and solve for the corresponding x and y values. This will give you the coordinates of the desired point on the line.

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