5x-6y=22 in slope intercept

Slope intercept form means that you have to solve for y.

Subtract 5x from both sides

5x - 6y - 5x = 22 - 5x

= - 6y = 22 - 5x

Then divide by - 6

-6y/-6 = 22/-6 - 5x/-6

= y = - 22/6 + 5x/6

You can reduce the fraction - 22/6 to - 11/3

y = - 11/3 + 5x/6

Then swap the order of your terms so it looks nicer and you don't have a negative in front

y = 5x/6 - 11/3