How can I get the intersection of these lines

In summary, the user is seeking help with finding the intersection of a line with a slope from a horizontal line. They have provided two attachments and have tried solving the problem using substitution, but have received an incorrect answer. Another user has pointed out that the first equation is incorrect and should have a negative gradient.
  • #1
median27
58
0

Homework Statement


Kindly view my 1st attachment. I need help to get the intersection of the highest line and the line extended by a slope from the horizontal line.


Homework Equations


y=mx+b
y-y1=m(x-x1)


The Attempt at a Solution


Kindly view my 2nd attachment.
By substitution, I always get the answer -1.87 which is obviously wrong. The answer should be lesser than -5.5.

Thanks in advance.
 

Attachments

  • Untitled.png
    Untitled.png
    9.8 KB · Views: 506
  • 1.png
    1.png
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  • #2
The first equation (y = x+105.5) is not quite correct. The gradient does have a magnitude of 1, however the line slopes downwards along the x-axis, therefore the gradient should be -1, not +1 as you have used. See if that fixes the problem.
 
  • #3
thanks, i'll work on it
 
Last edited:

1. How do I find the intersection point of two lines using equations?

The intersection point of two lines can be found by solving the equations of the two lines simultaneously. This can be done by setting the equations equal to each other and solving for both variables. The resulting values will be the coordinates of the intersection point.

2. Can I find the intersection point using only the slopes and intercepts of the lines?

Yes, the intersection point can be found by setting the slopes and intercepts of the two lines equal to each other and solving for the variables. However, this method may not work for lines that are parallel or coincident.

3. Is there a specific formula or algorithm for finding the intersection point of two lines?

Yes, there are several formulas and algorithms that can be used to find the intersection point of two lines. Some common methods include using the slope-intercept form, point-slope form, or the elimination method. The best method to use will depend on the specific equations of the lines.

4. What if the lines are not in standard form? Can I still find the intersection point?

Yes, you can still find the intersection point if the lines are not in standard form. You will need to rearrange the equations into either slope-intercept form or point-slope form and then solve for the variables using the methods mentioned earlier.

5. Are there any other factors that could affect the accuracy of finding the intersection point?

Yes, there are a few factors that could affect the accuracy of finding the intersection point. These include rounding errors in calculations, using approximate values for slopes and intercepts, and human error in solving the equations. It is always a good idea to double check your work and use precise values whenever possible to ensure accuracy.

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