Algebra writing 600 words due today
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Imagine that a line on a Cartesian graph is approximately the distance y in feet a person walks in x hours. What does the slope of this line represent? How is this graph useful? Provide another example for your colleagues to explain.
What are the differences among expressions, equations, and functions? Provide examples of each.
What is the most commonly used linear equation? We usually call this our “generic” equation or “common” linear equation. Why is this type of linear equation the most used form? How is it helpful to us and what do we use most often from it?
The question states the y is the feet a person walks, while x is the amount of hours. The slope of this line when represented on a graph indicates the distance in feet (y) and how long it takes a person to walk there in hours (x). The (y) coordinates will rise on the graph as the distance the person walks increases, while the (x) coordinates on the graph will stretch further horizontally to indicate the amount of time that it took the person to walk the distance, therefore showing the relationship between the two. This graph is useful because it makes a clear indication to how long it takes a person to walk a certain distance as well as allows future predictions to be made should the person have kept walking, as long as it is at a set interval. Another example of this would be. Imaging a line on a graph is approximately the amount of rain fall (y) that has fallen in a certain amount of minutes (x). What would the slope of this line represent?
The slope of the line represents how far a person has traveled and how long it has taken them to travel a certain distance. An example would be an athlete who is a distance runner and he wants to record his time and how long it has taken him to run a certain amount of miles. The slope would be the time it takes him to complete his run which would be the x intercept or the slope. The y intercept would be how far he has traveled and the miles he has run on that particular day. The slope would represent where the line intersects on the graph. This is a constant rate of change because the runner could run fast on one mile and slower on another miles. This would be useful in determining what times and how far he must run the next time to achieve his goals.
One thing we are discussing this week is functions. From past experience, I have seen many students become confused when we begin using function notation. Based on what you know from order of operations, why would function notation be confusing? For instance, if I had a function such as, f(x)=4x+5, and I asked you to find the function value when x=2, can you see a common mistake many students make when finding the answer? Start with looking for the answer yourself.
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