What is the equation of the line in standard form? x−2y=4 x + 2y = 4 2x−y=2 2x + y = 2

For this case we have that by definition, the equation of a line of the point-slope form is given by:[tex]y-y_ {0} = m (x-x_ {0})[/tex]Where:m: It's the slope[tex](x_ {0}, y_ {0}):[/tex] It is a point through which the line passesTo find the slope, we need two points through which the line passes, observing the image we have:[tex](x_ {1}, y_ {1}): (2,2)\\(x_ {2}, y_ {2}): (-1, -4)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-4-2} {- 1-2} = \frac {-6} {- 3} = 2[/tex]Thus, the equation is of the form:[tex]y-y_ {0} = 2 (x-x_ {0})[/tex]We choose a point:[tex](x- {0}, y_ {0}) :( 2,2)[/tex]Finally, the equation is:[tex]y-2 = 2 (x-2)[/tex]Now, we write the equation of the standard form [tex]ax + by = c[/tex]:[tex]y-2 = 2x-4\\y-2 + 4 = 2x\\y + 2 = 2x\\-2x + y = -2[/tex]This is equivalent to:[tex]2x-y = 2[/tex]Answer:[tex]2x-y = 2[/tex]Option C