Slope intercept form is a linear equation in the form of "y=mx+b" where m=slope of the line, and b=y-intercept of the line. To find the slope of a line, you will need to take the change in y and divide by the change in x. Most people refer to this as rise over run, since the change in y between two points is vertical, and the change in x between two points is horizontal.
Slope intercept form is used to express the equation of a straight line. The slope of a line is the steepness of the line, and the y-intercept of a line is the point at which the line crosses the y-axis. You can find the slope intercept form by looking at the graph of a straight line, or purely from knowing two points that are part of a straight line.
You can find the slope of a line if you know at least two points that lie on the line. The equation to find the slope of two points (x1,y1) and (x2,y2) is (y2-y1) / (x2-x1) or (y1-y2) / (x1-x2).
Here is a video that does a great job explaining slope-intercept form in depth.
This website does a great job of working through the process of graphing a line from a slope intercept equation.
Now that we have gone over what slope intercept form is, and what it is used for here are some practice problems.
Once you feel comfortable working through practice problems take a look at this video and work through these word problems with the aid of the video.
Slope-intercept form is used a lot throughout Algebra and other Math courses. It is even applicable in real-world scenarios and by understanding and being able to interpret graphs will go a long ways in life. This website shows examples of slope-intercept form being used in the real world.