Formative Reflection

1. I would find the rate of change of the story, and then find where the “y” starts (for example “Jack had 500 buckets of water at first”). Then, I would use the slope and y intercept to make the equation.
2. I would first use two “x and y” values to get the slope (y2-y1/x2-x1), then use (y2-y1/x2-x1) to solve for the x intercept, by making 0 one of the x values. Then, using the the y value found in the equation, I would use that to form the equation.
3. I would take two “x , y” values from the graph (e.g. 0,5 and 6,11), and plug it into the (y2-y1/x2-x1) equation to get the slope. Then, I would look on the graph to see where the line touches the y axis. If it is not clear, then I would use (y2-y1/x2-x1) to solve for the x intercept, by making 0 one of the x values. Then, like before, I would plug it into the equation.
4. I would place 0 into the x value in the equation, then solve for y. That would be my first point. Then, I would place another number in the x value, and solve for y. Then, I would have two points, and I would graph them.
5. If I am given a table of values, I would just take two points, plot them, and draw a line.
6. To derive y=mx+b using similar triangles, I would draw a triangle with the hypotenuse on the line on the graph. As all triangles that are similar to the triangle I just drew, I would find the two outer lengths of the triangle, which would be the slope. Then, I would see where it crossed the x axis. However, if I knew the slope, then I would know that all the triangles on the line would have the ratio 2:3 for the rise and run.  Then, I would know that the right triangle that (0,b) and (x,y) forms would have the ratio m:1. I would know that the horizontal side of the triangle is “x”, and “y” length of the triangle would be y minus b (y intercept). I would then know that (y-b/x)=m/1, which simplifies to y=mx+b.