Slope intercept form is just a way of writing a curve's equation so that the slope and the y intercept is really easy to find.
y=mx+b is the way we write slope intercept form. m is the slope (rise over run) and b is the y value where the curve hits the y axis.
So let's rearrange til the equation looks more like y=mx+b
2x+y=22 (from question)
Subtract 2x from both sides.
y=22-2x
y=-2x+22 (this is the answer to the question, you can stop here if you like)
Now we know some things about this straight line, firstly, it's straight line (x, not x^2 or anything like that), it goes downward from left to right and it is steep, every time we go 1 value along the x axis it goes down 2 values on the y axis. It also hits the y axis at +22.