I am going to be presenting at a technology in conference next weekend, February 21, 2015. The topic is integrating iPad apps into the classroom, your lesson plans while meeting state standards. After playing with Lion Grapher in the classroom, I know know the sequential use of the four modes will allow students to learn more about sloping and graphing.
Line mode would be first so they can move a line (y = -1x + 0) up, down, left or right to explore what happens to the y-intercept as the line moves. In addition, you can change the slope and sign for further exploration.
Point mode lets students put in two points and the app will map the portion of the line lying between the two points and it will provide the m part of the y=mx + b. This is a good way for students to check their math when they calculate slope by hand.
Intercept mode has the student input a point and the y intercept. It graphs the full line and shows the equation. This is a nice way for students to check their work after they've used the point slope form.
Lion Mode is great for calculating the slope off the graph because the student has to figure out the slope from the y intercept to the lion's head by counting square on the graph. This helps students develop a connection from the visual picture for the slope and the mathematical m.
The order I would do this in would be, Line mode, Lion mode, point mode and intercept mode. I like this app a lot but my kids don't like it only because they find it difficult to use the app at first. Once they have the hang of using it, they like it.