Write an equation in slope-intercept form of the line through points (6,62 and (5,53)

The formula for finding slope when given two points on the line is
m=(y-y)/(x-x) 
it doesn't really matter which x and y you use first but it needs to be consistent. 
so if you use 62 as the first y, you must use 6 as the first x.
so using 62 as the first y you can do
m=(62-53)/(6-5) 
m= 9/1
m=1
now that we have the slope we can being to assemble the formula
slope intercept form is y=mx+b when m=slope and b= y-intercept
now the equation will be 
y=9x+b
since you are missing the y-intercept, you can plug in one of your coordinates that you do have for x and y and then solve for b
53=9(5) + b
53=45 + b
8=b
now that you have b you can finish the equation
y=9x+8