The slope-intercept form is, by far, the most commonly used form for linear equations because it is so easy to graph a function just by looking at it. The slope-intercept form is:
y=mx+b,
where m is the slope and b is the y-intercept. When we are given the slope and y-intercept, we can simply substitute them into the formula. When we are looking at a graph, we can also easily write the equation by looking for the slope and y-intercept. Let's look at an example graph.
Looking at this linear function, we can see that it crosses the y-axis at (0,1) which means that the y-intercept is 1. We can also see that as the function moves 1 step up, it moves 3 steps to the right, our "rise over run" is 13. We can then substitute those pieces of information into our formula and we get:
y=1/3x+1.
