Question

How do you write an equation in point slope form given (8,3), (-1/3,-2)?

Answer 1

See the entire solution process below:

Explanation:

First, we need to determine the slope f 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)(-2) - color(blue)(3))/(color(red)(-1/3) - color(blue)(8)) = (-5)/(color(red)(-1/3) - color(blue)(24/3)) = ((-5)/1)/((-25)/3) = (-5 xx 3)/(1 xx -25) =`

`(-1 xx 3)/(1 xx -5) = (-3)/-5 = 3/5`

Now, we can use the point-slope formula to write the equation. 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 first point from the problem gives:

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

Or. we can substitute the slope we calculated and the second point from the problem giving:

`(y - color(red)(-2)) = color(blue)(3/5)(x - color(red)(-1/3))`

`(y + color(red)(2)) = color(blue)(3/5)(x + color(red)(1/3))`