To write in slope-intercept form, you first need to get y by itself. To do this, subtract 7x from both sides of the equation.
Doing this gets you: y = 25 - 7x
Now that y is by itself, remember that slope-intercept form looks like this: y = mx + b
So, let's switch the right side.
y = -7x + 25
Slope intercept form is: y = -7x + 25
Rules for y in Slope-Intercept form:
y must be positive
y must be by itself (so, not 2y, or anything with it... just y)