Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
We have the point (3, -3) and the slope m = -2. Substitute:
[tex]y-(-3)=-2(x-3)[/tex]
[tex]y+3=-2(x-3)[/tex] - point-slope form
Convert to the slope-intercept form (y = mx + b):
[tex]y+3=-2(x-3)[/tex] use the distributtive property
[tex]y+3=-2x+(-2)(-3)[/tex]
[tex]y+3=-2x+6[/tex] subtract 3 from both sides
[tex]y=-2x+3[/tex] - slope-intercept form
Convert to the standard form (Ax + By = C):
[tex]y=-2x+3[/tex] add 2x to both sides
[tex]2x+y=3[/tex] - standard form
Convert to the general form (Ax + By + C = 0):
[tex]2x+y=3[/tex] subtract 3 from both sides
[tex]2x+y-3=0[/tex] - general form
