Question

How do you write the point slope form of the equation given (3,4) and (-7,4)?

Answer 1

See a solution process below:

Explanation:

Because both of the `y` values are the same this is, by definition a vertical line. A vertical line has the same `y` value for each and every value of `x`.

The slope of a vertical line, also by definition is `0`:

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 use this slope and the values from either of the points in the problem to write the point-slope formula as:

`(y - color(red)(4)) = color(blue)(0)(x - color(red)(3))`

Or

`(y - color(red)(4)) = color(blue)(0)(x - color(red)(-7))`

`(y - color(red)(4)) = color(blue)(0)(x + color(red)(7))`

We can also, write this equation in the generic form of:

`(y - color(red)(4)) = color(blue)(0)(x + color(green)(a))`

Where `color(green)(a)` is an value you want to select.