Question

How do you write the point slope form of the equation given (0,4) and (1,-4)?

Answer 1

`(y - color(red)(4)) = color(blue)(-8)(x - color(red)(0))`

Or

`(y + color(red)(4)) = color(blue)(-8)(x - color(red)(1))`

Explanation:

First, we need to 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 two points in the problem gives:

`m = (color(red)(-4) - color(blue)(4))/(color(red)(1) - color(blue)(0))`

`m = -8/1 = -8`

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.

Solution 1) Using the calculated slope and the values from the first point in the problem gives:

`(y - color(red)(4)) = color(blue)(-8)(x - color(red)(0))`

Solution 1) Using the calculated slope and the values from the second point in the problem gives:

`(y - color(red)(-4)) = color(blue)(-8)(x - color(red)(1))`

`(y + color(red)(4)) = color(blue)(-8)(x - color(red)(1))`