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- anonymous

Line m has the equation 3y = 6 + y. Line n is perpendicular to line m and contains the point (4, –2). When graphed, what is the point of intersection for lines m and n? Please explain.

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- anonymous

(4,3)

- Directrix

Line m has equation 3y = 6 + y. This simplifies to 2y = 6 and then y = 3.
y = 3 is a horizontal line. Any value of x has a y-value of 3.
If line n is perpendicular to line m, the line n has to be a vertical line. On a vertical line, all the x values are the same. In this case, x = 4 because the line n passes through the point (4, -2). On a vertical line, the value of y can be any real number.
The question now is where does the line x = 4 intersect the line y = 3? That would have to be the point (4,3).

- Directrix

The graphs are sketched at this link:
http://www.wolframalpha.com/input/?i=%28x+%3D+4%29+and+%28y+%3D+3%29

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- Directrix

Questions?

- anonymous

Thank you

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