Question

How do you write the equation in point slope form given (4,0) and (0,5)?

Answer 1

`(y - color(red)(0)) = color(blue)(-5/4)(x - color(red)(4))`

Or

`(y - color(red)(5)) = color(blue)(-5/4)(x - color(red)(0))`

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)(5) - color(blue)(0))/(color(red)(0) - color(blue)(4)) = 5/-4 = -5/4`

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 calculate and the first point from the problem gives:

`(y - color(red)(0)) = color(blue)(-5/4)(x - color(red)(4))`

We can also substitute the slope we calculate and the second point from the problem giving:

`(y - color(red)(5)) = color(blue)(-5/4)(x - color(red)(0))`