Question

How do you write the equation of a line in point slope form and slope intercept form given points (2, 7) (1, -4)?

Answer 1

The slope of the line segment between two points is the change in `y` divide by the change in `x`.

For the case of a line through `(2,7)` and `(1,-4)` we have

slope `m = (Delta y)/(Delta x) = (-4-7)/(1-2) = -11/-1 = 11`

Using the point `(2,7)` we can write the equation of the line in point slope form as:

`y-7 = m(x - 2)` where the slope `m = 11`.

That is:

`y - 7 = 11(x - 2)`

To get point intercept form, first expand the right hand side so...

`y - 7 = 11x - (11*2) = 11x - 22`

Then add `7` to both sides to get:

`y = 11x - 15 = 11x + (-15)`

This is point intercept ( `y = mx+c` ) form with slope `m = 11` and intercept `c = -15`.