Simple math.
There are several forms for this.
I'll use one for your question.
y – y1 = m(x – x1)
where,
(x1, y1) = (-5, 1)
or
x1 = -5 and y1 = 1
therefore,
y - 1 = 1/4 (x - (-5))
Compute.
y - 1 = 1/4x + 5/4
Multiply both sides by 4 to eliminate fraction for easy computation
4(y - 1) = 4(1/4x + 5/4)
4y - 4 = x + 5
Move 4 to the right and change sign
4y = x + 5 + 4
Compute
4y = x + 9
Then divide both sides by 4 to eliminate the 4 in 4y.
(4y)/4 = (x + 9)/4
y = 1/4x + 9/4
You have it
I hope it helps.