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
We ahve the slope m = 1/2 and the point (-2, 1). Substitute:
[tex]y-1=\dfrac{1}{2}(x-(-2))[/tex]
[tex]y-1=\dfrac{1}{2}(x+2)[/tex] - point-slope form
Covert to the slope-intercept form (y = mx + b):
[tex]y-1=\dfrac{1}{2}(x+2)[/tex] use the distributive property
[tex]y-1=\dfrac{1}{2}x+1[/tex] add 1 to both sides
[tex]y=\dfrac{1}{2}x+2[/tex] - slope-intercept form
Convert to the standard form (Ax + By = C):
[tex]y=\dfrac{1}{2}x+2[/tex] multiply both sides by 2
[tex]2y=x+4[/tex] subtract x from both sides
[tex]-x+2y=4[/tex] change the signs
[tex]x-2y=-4[/tex] - standard form
Convert to the general form (Ax+By+C=0):
[tex]x-2y=-4[/tex] add 4 to both sides
[tex]x-2y+4=0[/tex] - general form
