Question

How do you write an equation in point slope form given (2p, -q), (p, p-q)?

Answer 1

See the entire solution process below:

Explanation:

First, you must determine the slope of the line. The slope can be found by using the formula: `m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))`

Where `m` is the slope and (`color(blue)(x_1, y_1)`) and (`color(red)(x_2, y_2)`) are the two points on the line.

Substituting the values from the points in the problem gives:

`m = (color(red)(p-q) - color(blue)(-q))/(color(red)(p) - color(blue)(2p)) = (color(red)(p-q) + color(blue)(q))/(color(red)(p) - color(blue)(2p)) = (p - 0)/-p = p/-p = -1`

The point-slope formula states: `(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))`

Where `color(blue)(m)` is the slope and `color(red)(((x_1, y_1)))` is a point the line passes through.

Now, substitute the slope you calculated and the values for the first point in the problem to give:

`(y - color(red)(-q)) = color(blue)(-1)(x - color(red)(2p))`

`(y + color(red)(q)) = color(blue)(-1)(x - color(red)(2p))`

Or, substitute the slope you calculated and the values for the second point in the problem to give:

`(y - (color(red)(p-q))) = color(blue)(-1)(x - color(red)(p))`