Animating Slope and Y-Intercept

Abstract

In 8th grade math, we investigate graphing lines from equations for the first time. Students learn about the xy coordinate plane, the table of values, the slope and the x and y intercepts. They begin to understand y = mx + b, the general equation for a line. As a teacher, I have encountered many problems while teaching this content without the benefits of technology. It’s my goal to teach the effects of changing the slope and the y-intercept. With traditional methods, we create a table of values and draw a graph by hand, which consumes a lot of instructional time. By the time the graphs are made, if the students are careful, they can draw some conclusions about slope and y-intercept. The first graphs that 8th grade students create usually are not usually accurate enough to learn the concepts from. It’s also a challenge to have students stay focused on discovering the effects of slope and y-intercept when there are many potential mistakes in the table and graph alone. As my Challenge Project topic, I wanted to create a model that would show a more efficient, visual representation of the effects of slope and the y-intercept on the graph of a line. To create models that illustrate this area of the curriculum, we used the TI graphing calculators and the Geometer’s Sketchpad software. The students began to graph lines using the calculator. It addressed the following the New York State Standards. Students will: 8.G.13 Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change, 8.G.14 Determine the y-intercept of a line from a graph and explain the y-intercept. 8.G.17 Graph a line from an equation in slope-intercept form (y = mx + b) As they understood the concepts, we worked with Project Interactivate and found that our conclusions were correct. The combination gives the students a variety of different technologies and models to get understanding from.