Writing Equations Given Two Points or Slope and One Point

In my experience, this topic is a challenging one for algebra students every year. 

Students try to memorize the rules involved in each situation.  Then, they become frustrated by the amount of information they are trying to remember.

I’ve come to the conclusion that the best approach is to teach this from a problem-solving perspective.  My students have seemed to do better since I have been focusing on this.  They can still memorize the step-by-step rules if that works better for them.

Here’s how I ask students to approach this lesson:

•    Look at the given information.
•    Using slope-intercept form (y = mx + b), the information should represent three of the four variables.  Which of the three variables can you substitute numbers for? 

•    Solve for the remaining variable.
•    Write the resulting equation in slope-intercept form or standard form.

Remember, this is entirely about how to analyze the given information in order to problem solve.  It is not about following a learned series of steps.  

Try it out and let me know how it goes!