Question

How do you write the point slope form of the equation given (-3,1) and (5,4)?

Answer 1

See a solution process below:

Explanation:

First, 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)(4) - color(blue)(1))/(color(red)(5) - color(blue)(-3)) = (color(red)(4) - color(blue)(1))/(color(red)(5) + color(blue)(3)) = 3/8`

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.

Substituting the slope we calculated and the values from the first point in the problem gives:

`(y - color(red)(1)) = color(blue)(3/8)(x - color(red)(-3))`

`(y - color(red)(1)) = color(blue)(3/8)(x + color(red)(3))`

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

`(y - color(red)(4)) = color(blue)(3/8)(x - color(red)(5))`