We need to find which of the equations has a slope of 1/4
At first we should know that, the general form of the slope intercept form is
y = mx + b
Where m is the slope
So, we will check the options:
I. y = 1/4 x - 5
Compare to the general form
so, the slope = 1/4
II. ( y - 3.5) = 0.25 ( x - 2.75)
so,
y - 3.5 = 0.25x - 0.25 * 2.75
y = 0.25x -2.25 * 2.75 + 3.5
so, the slope = 0.25
III. 5x - 20y = 32
-20y = -5x + 32
Divide all terms by -20
y = (-5/-20) x - 32/20
y = 0.25 x - (32/20)
so, the slope = 0.25
IV. 5x + 20y = 32
20y = -5x + 32
Divide all terms by 20
y = (-5/20) + 32/20
y = -0.25 x + (32/20)
so, the slope = -0.25
As a result
The answer is option h). I , II and III only