The equation of the line that passes through is Y=-2x-2
Step by step:
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]m = \frac{ - 4 - 2}{1 - - 2} \: or \: m = \frac{ - 6}{3} \: or \: m = - 2[/tex]
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
[tex]y = - 2x + b [/tex]
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(-2,2). When x of the line is -2, y of the line must be2.
(1,-4). When x of the line is 1, y of the line must be-4.
Now plug in x and y
You can use either (x,y) point you want..the answer will be the same:
(-2,2). y=mx+b or 2=-2 × -2+b, or solving for b: b=2-(-2)(-2). b=-2.
(1,-4). y=mx+b or -4=-2 × 1+b, or solving for b: b=-4-(-2)(1). b=-2.
See! In both cases we got the same value for b. And this completes our problem.
The equation of the line that passes through the points (-2,2) and (1,-4) is:
[tex]y = - 2x - 2[/tex]
