BC: James quickly understood how the y-intercept and slope could be used to write the equation of a line. He used the formula y=mx+b, where m was the slope of the line and b was the y-intercept.
FC: Linear Functions and the Coordinate Plane
1: James was eager to complete his assignment in his middle school math class. He was beginning a lesson on linear functions. Before he could learn about the slope and y-intercept of a function, he had to review what he knew about the coordinate plane.
2: James began by reviewing the basic areas of the coordinate plane. He knew the coordinate grid was two lines known as axes. The x-axis cuts the plane in half horizontally and the y-axis cuts the plane vertically. The intersection of these axes is called the origin. It has a coordinate of (0,0).
4: He also remembered that the x-axis and y-axis cut the coordinate plane into 4 regions called quadrants. Quadrant I was located in the top, right region and each quadrant was numbered counterclockwise.
6: Next, James looked up how to graph an ordered pair. He saw that each ordered pair had two numbers, an x-coordinate and a y-coordinate. Starting at the origin, he used the x-coordinate to determine how for right or left to plot the point. The y-coordinate told James how far up or down to plot the coordinate. James practiced by plotting (6,-5) on the coordinate plane. He showed his work on the right.
8: Finally, it was time for James to start learning about how linear functions are graphed on the coordinate plane. The first new vocabulary word he discovered was y-intercept. The y-intercept is the point on the line where a linear function crosses the y--axis. An example in his textbook showed a line with a y-intercept of 3.
10: The other important term that was mentioned by James' math teacher was slope. The teacher described slope as a measure that states the steepness of a line. Lines that have an upward trend are said to have a positive slope and lines with a downward trend have a negative slope.
12: The teacher then went over an example of how to calculate the slope of a plotted line. He showed students how count the rise and run of the line. Finally, the students used the rise and run to create a fraction that represented the slope of the line.