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##.Poetria said:It has been marked as wrong by an automatic grader. But I don't understand why. :(
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.
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.
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.
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.
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.