Answer:
[tex]\large\boxed{y-4=\dfrac{1}{2}(x+2)\text{- point-slope form}}\\\boxed{y=\dfrac{1}{2}x+5\text{- slope-intercept form}}[/tex]
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 have the slope [tex]m=\dfrac{1}{2}[/tex] and the point [tex](-2, 4)[/tex].
Substitute:
[tex]y-4=\dfrac{1}{2}(x-(-2))[/tex]
[tex]y-4=\dfrac{1}{2}(x+2)[/tex] - point-slope form
Convert to the slope-intercept form (y = mx + b):
[tex]y-4=\dfrac{1}{2}(x+2)[/tex] use the distributive property
[tex]y-4=\dfrac{1}{2}x+1[/tex] add 4 to both sides
[tex]y=\dfrac{1}{2}x+5[/tex] - slope-intercept form
