Question

Write an equation that is in slop-intercept form of the line that passes through the points: (-1/2, -1) and (3, 5/2).

Answer 1

Use your slope formula
(-1 - 2.5) / (-.5 - 3) = -3.5/-3.5 = 1

Pick a point, does not matter which one, will get the same answer and use your point slope equation

y - 2.5 = 1(x - 3)
y = x - .5
y = x - (1/2)

Answer 2

m = (y2-y1)/(x2-x1)
5/2-(-1)/(3-(-1/2)=
(7/2)/7/2 =1
so slope of the equation is 1.
No substitute one of the points into point slope equation and solve into slope intercept form:
y-y1 =m(x-x1)
y-(-1)=1(x-(-1/2)
y+1=x+1/2
y = x-1/2