Question

Write the equation in slope-intercept form of the line that contains the points (4, -7) and (0, 5).

Answer 1

subtract y2 from y1 and divide the answer by x2-x1
[-3]
y = -3x + c so far
insert values of x and y in coordinate [0, 5] into equation to find c
5 =-3[0]+c
8 = 0 + c
c= 8

hence answer is y = 8 -3x

Answer 2

Error alert!!! [well it is late in France!]

subtract y2 from y1 and divide the answer by x2-x1
[-3]
y = -3x + c
so far insert values of x and y in coordinate [0, 5] into equation to find c
5 =-3[0]+c
5 = 0 + c
c= 5
hence answer is y = 5 -3x

Answer 3

slope-intercept should look like:
y=-3x+5
this is just a matter or presenting the answer.
your solution is correct!