Equation for a line through an origin

In summary, the conversation discusses a mathematical expression being marked as wrong by an automatic grader. The issue is related to the lack of a unique solution and the possibility of different solutions being valid. It is suggested to try a positive value for one of the variables to see if that satisfies the grader's criteria.
  • #1
Poetria
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Homework Statement
Find the equation for the line through the origin that is perpendicular to the vector (-1,4). Enter the equation in the form: ##a*y+b*x=0##
Relevant Equations
Dot product of the vector (-1,4) and the vector parallel to the line has to be 0.
Why is this wrong?
$$-4*y+x=0$$

$$\vec (-1, 4)\cdot\vec (4,1)=0$$
 
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  • #2
Why do you think it is wrong?
 
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  • #3
It has been marked as wrong by an automatic grader. But I don't understand why. :(
 
  • #4
Poetria said:
It has been marked as wrong by an automatic grader. But I don't understand why. :(
There is no unique solution to ##ay+bx=0## because all ##acy+acx=0 \;(c\neq 0)## are solutions, too. Could be that whatever checked it expected a normalized vector, or a positive ##a##.
 
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  • #5
It is stated: expression in the form ##a*y+b*x##. I will try with the positive a then.

$$4*y-x=0$$

Many thanks. :)
 
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FAQ: Equation for a line through an origin

What is the equation for a line passing through the origin?

The equation for a line passing through the origin is y = mx, where m is the slope of the line. This means that the y-intercept is 0, since the line passes through the origin where both x and y coordinates are 0.

How do you find the slope of a line through the origin?

To find the slope of a line through the origin, you need to first identify two points on the line. Then, you can use the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Since the line passes through the origin, one of the points will be (0, 0). This will result in a slope of 0, as any number divided by 0 is undefined.

Can the equation for a line through the origin be written in standard form?

Yes, the equation for a line through the origin can be written in standard form as Ax + By = 0, where A and B are constants. Since the y-intercept is 0, the equation can be simplified to Ax = 0, where A is the slope of the line.

How does the equation for a line through the origin differ from the general equation for a line?

The equation for a line through the origin, y = mx, is a special case of the general equation for a line, y = mx + b. The main difference is that the y-intercept, b, is equal to 0 in the equation for a line through the origin. This means that the line passes through the origin, rather than intersecting the y-axis at a different point.

Can the equation for a line through the origin be used to represent a vertical line?

No, the equation y = mx for a line through the origin cannot be used to represent a vertical line. This is because the slope, m, would be undefined for a vertical line, as any number divided by 0 is undefined. Therefore, the equation for a vertical line passing through the origin would be x = 0.

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