Question

How do you write the point slope form of the equation given (1,9) and (-2,-2)?

Answer 1

See the entire solution process below:

Explanation:

First, we must determine the slope. 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)(-2) - color(blue)(9))/(color(red)(-2) - color(blue)(1)) = (-11)/(-3) = 11/3`

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 now substitute the slope we calculated and the values from the first point giving:

`(y - color(red)(9)) = color(blue)(11/3)(x - color(red)(1))`

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

`(y - color(red)(-2)) = color(blue)(11/3)(x - color(red)(-2))`

`(y + color(red)(2)) = color(blue)(11/3)(x + color(red)(2))`