Question

Could someone please explain to me how to solve this question?

Write the equation of the line, in point-slope form. Identify the point (-2, -2) as (x1, y1).

Answer 1

`y+2 = x+2`

Explanation:

A line is written in the point-slope form if its equation is in the form

`y-y_1 = m(x-x_1)`

where

`m=(y_2-y_1)/(x_2-x_1)` is the slope of the line, calculated using the two points
`(x_1,y_1)` and
`(x_2,y_2)`

In this problem, we have the following two points:

`(x_1,y_1) = (-2,-2)\\(x_2,y_2)=(2,2)`

Therefore we can calculate the slope of the line:

`m=(y_2-y_1)/(x_2-x_1)=(2-(-2))/(2-(-2))=(4)/(4)=1`

And so, the equation of the line in point-slope form is

`y-(-2) = 1(x-(-2))\\\rightarrow y+2 = x+2`