Finding the Equation of a Graphed Line - Concept
Sometimes we'll be given a graph of a line, and told to find the equation. There are many methods of finding the equation of a line with only a graph such as finding the slope and a point or finding two points. In order to understand finding the equation of line with its graph, one should understand the different forms of an equation of a line, especially point-slope and slope-intercept form.
Alright guys this one of the most important skills you're going to get out of your Algebra one class. And that is when you're given a graph you're asked to write the equation that created that graph. A lot of the times we do it backwards. Most people are pretty good at taking an equation and drawing the graph of it here you have to do it backwards someone is going to you a graph you're going to be asked to write the equation. So let's think about what that means, you know a bunch of different forms of equations for lines. One really commonly used form is the slope intercept form, for me personally this is my favorite form I think graphs are easiest to think of in terms of their slope and their y intercepts.
So if you wanted to write an equation in this form you need two things you need to find the slope and you need to find the y intercept. If you can find those two things you can do the equation really quickly.
If you want to use this, the point slope form again you're going to need to find a point and a slope hence the name. To use this equation you need the point and the slope. So no matter how you go about writing the equation you're going to have to find the slope and you know the y intercepts or one of the other points. Keep in mind what you guys know about finding a slope if you know two points on the line, you can use this equation to find the slope or if the line is drawn on graph paper a shortcut I like to use is just counting the vertical rise putting that on top of the horizontal run to find the slope it's like using a slope triangle.
So when you guys are given a graph and you're asked to write an equation, keep in the back in your mind you have some options. You can either find the slope in the intercept y intercept or you can find the slope at any of point you want to and then once you have any of those pairs of information you can go through and find the equation for the line.