Standard form shows the x and the y on one side with their respective coefficients.
So, for example, x + y = 5
Every x and y pair that you plug in which makes this true forms a point on a graph, and if you draw a line through these points it is a perfect straight line.
slope intercept form is y = mx + b, where m is the slope, and b is the y value at the y intercept
It is more suited to plugging in an x value and receiving the y (or height) at that location, and you can easily write down any straight line you see with this equation.
-Jeron