Question

How do you write the equation in point slope form given (2, 5) and (–1, 8)?

Answer 1

See a solution process below:

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)(8) - color(blue)(5))/(color(red)(-1) - color(blue)(2)) = 3/-3 = -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.

We can substitute the slope we calculated and the values from the first point in the problem giving:

`(y - color(red)(5)) = color(blue)(-1)(x - color(red)(2))`

We can also substitute the slope we calculated and the values from the second point in the problem giving:

`(y - color(red)(8)) = color(blue)(-1)(x - color(red)(-1))`

`(y - color(red)(8)) = color(blue)(-1)(x + color(red)(1))`