Question

How do you write an equation in point-slope form for the given (-2, -1), (4, -4)?

Answer 1

Determine the slope from the 2 points then use that together with one of the points to write the point-slope form equation

Explanation:

Step 1: Find the slope of the line through `(-2,-1)` and `(4,-4)`
Given two points `(x_1,y_1)` and `(x_2,y_2)` the slope of the line through them is:
`color(white)("XXXX")` `m = (y_2-y_1)/(x_2-x_1)`

For the given values this becomes:
`color(white)("XXXX")` `m = (-4 - (-1))/(4-(-2)) = -1/2`

Step 2: Insert the calculated slope and one of the points into the general slope-point form
The general slope-point form is
`color(white)("XXXX")` `y-haty = m(x-hatx)`
`color(white)("XXXX")` `color(white)("XXXX")`for a line with slope `m`
`color(white)("XXXX")` `color(white)("XXXX")`through the point `(hatx,haty)`

Using `(-2, -1)` as `(hatx, haty)` and the slope from Step 1:
`color(white)("XXXX")` `y-(-1) = (-1/2)(x-(-2))`