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Complete your Week 3 discussion prompt:

One application of algebra in real-life is identifying patterns between two events that seem related (known in mathematics as a correlation). The image below shows a scatter plot (an xy graph containing only points) that shows a relationship between the nurses’ work experience and their annual salaries. Each point in the scatter plot is matching a nurse’s years of work experience with the annual salary earned by that nurse. For example, the point (4, 45) in the scatter plot below, it represents a nurse with 4 years of experience that is earning $45,000 per year.

Now, if you observe carefully the scatter plot, you will see that most of the points are arranged somewhat in a straight line. From this observation, we can infer (conclude) that the annual salary of a nurses has a linear relationship with their years of work experience.

If you look again the scatter plot, you will notice most of the points resemble a straight line that is going up from left to right. This means the following: “The more years of work experience a nurse has, their annual salary increases proportionally (constant rate) per year.” We say this relationship has a positive slope.

From scatter plots such like the one above, we can create a linear equation (known also as a linear model) to help us make predictions of the salary of any nurse based on their work experience.

This discussion has two parts:

(1) Your task is to find the linear equation that represents the scatter plot above by doing the following:

(a) Select any two points from the scatter plot (that has not been chosen from your classmates). List these two points as an ordered-pair: (x1,y1) and (x2,y2).

(b) Calculate the slope of line that the scatter plot resembles by using the two points you selected above. Show work. 

(c) Using the slope-intercept formula y = mx + b, calculate the value of b (also known as the y-intercept). Show work.

(d) Using again the slope-intercept formula y = mx + b, replace the variables m and b by using the values you got in steps 2 & 3 to set up the equation of the line the scatter plot resembles. What is the equation that you found?

(e) Using the equation you found in step 4, make a prediction of the annual salary of a nurse who has 22 years of work experience. Is your answer different than what the scatter plot above shows with the point (22, 60)? Explain why or why not.

(2) Using the internet, find a scatter plot that resembles a line and create a similar exercise (as you did in part 1 above) for your classmates to try.