Question

How do you write the equation in point slope form given (5,6) and (10, 9)?

Answer 1

`(y - color(red)(6)) = color(blue)(3/5)(x - color(red)(5))`

Or

`(y - color(red)(9)) = color(blue)(3/5)(x - color(red)(10))`

Explanation:

First, we need to 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)(9) - color(blue)(6))/(color(red)(10) - color(blue)(5)) = 3/5`

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.

Substituting the slope we calculated and the first point gives:

`(y - color(red)(6)) = color(blue)(3/5)(x - color(red)(5))`

We can also substitute the slope we calculated and the second point giving:

`(y - color(red)(9)) = color(blue)(3/5)(x - color(red)(10))`