How to Graph a Line using y=mx+b - Concept
When given an equation in the form y = mx + b, or slope-intercept form, we should know how to graph a line without having to compute two points on it. If we have an equation in slope-intercept form, we automatically know the slope and the y-intercept and can use that information to more quickly and efficiently graph the line. Another method of graphing a line is using a table of values or the intercepts.
When you're asked to graph a line, you have three big options on how you want to approach it. The first option is to make an xy table of values, where you choose x values and you substitute them in one by one to find the corresponding y values, and then plot those points on the graph. For me that takes all day. I don't like that method.
The second option you have is to use y=mx+b strategies and this is really useful if your equation is already in slope intercept form like this or if it's close to that and you just need to do a little bit of solving. This is my personal favorite method. Here's is how it goes. Your first dot goes on the y axis at the y intercept. From there you count the slope and make another point and then you just connect them. That's my favorite and that's what we're going to be practicing more in your homework these days.
The third option you have is to find and connect to the x and y intercepts. The way you find the x intercept is by substituting in in y=0 and to find the y intercept you substitute in x=0. So that's a good option. Most people like this method if the equation's given to you in standard form. You always have a choice and you could always kind of barrel through any one of these methods. But one of the signs of a more advanced student is a student who knows how to choose a different method for the appropriate problem and to be able to justify why he chose that method. So that's something to keep in mind. All of these will work but for any given problem one method will be way easier than the others. That's something we're going to be practicing as you guys work through your homework problems.