What is slope-intercept form? why do we write equations using this form?

Slope intercept form is y=mx+b
m=slope
b=y-intercept

the slope is the rate of change of the graph, basically rise/run (change in y divided by change in x)

the y intercept is where the graph intercepts the y axis

we usually use this form because we can find the slope and find where it hits the y axis.
there are other forms that may be helpful later on, but this one is usually the easiest form to find from a graph