We are given the point-slope form of a line: `y-4=3(x+1) ` . We are then asked to find the ordered pair (coordinates) of the point lying on a line parallel to the given line with x value 2. (Note this is the same as finding the intersection of the vertical line x=2 and the constructed line parallel to the given line.)

From the alternate description of the question, it is clear that there are an infinite number of answers. The line x=2 will intersect every line parallel to the given line.

First note that the slope of the given line is 3. (We also know that it passes through the point (-1,4).) Every line with slope 3 is parallel to this line, and as stated above each of these lines will intersect the vertical line x=2.

Assume the coordinates of the point of intersection between the constructed lines and the line x=2 are of the form (2,k), where k is a real number. **Then the point-slope form for every line of this type is y-k=3(x-2)**

Here are some graphical examples:

The red line is the original line (with a slope of 3, containing (-1,4)). The black lines are parallel to the red line, and you can see, from top to bottom, that they intersect x=2 at (2,19), (2,16), (2,13), (2,11), (2,9), and (2,7) respectively.

** If there was more information given in your original problem, you could pinpoint which of these lines was required. For example, if the line goes through the origin, the equation would be y=3(x-2). **

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**Further Reading**

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