Finding Inclination of Line: x = [a number]

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In summary, the problem involved finding the equation of a line that divides the angles of a triangle in half. The given information included equations for three lines, one of which was the line BC. The process involved finding the slope of two lines, B and C, and using it to find the coordinates of point A. The final result was that the line AB was perpendicular to the X axis and had an equation of x = 5.
  • #1
Chen
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(I don't study math in English so I'm not sure what the exact terms are... please bear with me. :))

If you have this line:
y = mx + n
m is the inclination of the line, right? And I have this equation to find m:
2m + 1 = 2m + 4 (I'm finding a line between two other lines that divides the angle in half)
Obviously no m can solve that equation - this means that the line is reall of the form:
x = [a number]

Am I correct?
 
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  • #2
Knowing only what you've written here, my best guess is that you're correct. What was the entire problem?


P.S. we would call m the slope of the line.
 
  • #3
The whole problem was this:

You have a triangle ABC, with BC on the line:
3x - 4y + 37 = 0 (BC)
And then you also have the equations for the two lines that divide the angles B and C of the triangle:
2x - y + 3 = 0 (BE)
x + 7y - 4 = 0 (CF)

I solved it by finding the slope of both AB and AC, and then finding B and C, and then finding the equations of AB and AC, and finally finding the coordinates of A.

To find m (slope of AB) I did this: (based on the given that the angle between AB and BE is the same as the angle between BE and BC)
(2 - m) / (1 + 2m) = (3/4 - 2) / (1 + 6/4) = -1/2
-4 + 2m = 1 + 2m
-4 = 1

And from this I deduced that the line AB is perpendicular (sp?) to the X axis. I found B to be (5, 13) and since it is on the AB line I figured that AB was x = 5.

Thanks for the help. :-)
 
Last edited:

1. What is the meaning of "inclination of a line"?

The inclination of a line refers to the angle at which the line is tilted or slanted on a graph. It can also be interpreted as the slope or steepness of the line.

2. How do I find the inclination of a line given the equation "x = a number"?

Since the equation x = a number represents a vertical line passing through the x-axis at a specific point, the inclination of this line is undefined. This is because the slope of a vertical line is infinite and cannot be represented as a single number.

3. Can I use the y-intercept to find the inclination of a line with the equation "x = a number"?

No, the y-intercept does not exist for a vertical line. The y-intercept is the point where the line intersects the y-axis, but a vertical line does not intersect the y-axis at any point.

4. How can I determine the inclination of a line using its graph?

To find the inclination of a line from its graph, you can use the slope formula, which is the change in y divided by the change in x. This will give you the slope or inclination of the line at any given point on the graph.

5. Is it possible for a line with the equation "x = a number" to have a positive or negative inclination?

No, since the equation x = a number represents a vertical line, its slope or inclination is undefined and cannot be positive or negative. The concept of positive or negative inclination only applies to lines with a finite slope, not vertical lines.

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