Writing a Linear Equation to Fit Data Draw a line that fits or models a set of points Write an intercept equation that fits a set of real-world data

A Health Connection

Both groups will set up the axes so Part of the group will create the graph on a Communicator® while the other part uses their graphing calculator. Both groups will set up the axes so saturated fat – x axis total fat – y axis Does the graph show a linear pattern? On the communicator® select the two points (8,21) and (38,90) and draw a line through these two points. Calculate the slope of this line. Write the equation of the line in the form y=bx. Enter this equation on the calculator. Adjust the y-intercept using the intercept form for a straight line: y=a+bx. Adjust the a value by tenths.

Predict the total fat in a burger with 20 grams of saturated fat. What is the real-world meaning of the y- intercept? What is the real world meaning for the slope? Predict the total fat in a burger with 20 grams of saturated fat. Predict the saturated fat in a burger with 50 grams of fat.

Analyzing the Exercises Problem 4 on page 230. Use your graphing calculator to investigate this exercise. After completing the exercise discuss How you used the data in the problem to determine find the value for slope (b). What did the value for a do to the line.

Point-Slope Form of a Linear Equation Learn the point-slope form of an equation of a line Write equations in point-slope form that model real-world data

You have been writing equations of the form y = a + bx You have been writing equations of the form y = a + bx. When you know the line’s slope and the y-intercept you can write its equation directly in intercept form. But there are times that we don’t know the y- intercept. Some homework questions had you work backwards from a point using the slope until you found the y-intercept. We can use the slope formula to generate the equation of a line from knowing the slope and one point on the line.

Since the time Beth was born, the population of her town has increased at the rate of approximately 850 people per year. On Beth’s 9th birthday the total population was nearly 307,650. If this rate of growth continues, what will be the population on Beth’s 16th birthday?

Because the rate of change is approximately constant, a linear equation should model this population. Let x = the time in years since Beth’s birth Let y = the population We know that the slope is 850 and one point is (9, 307,650) and another point on the straight line could be (x,y).

Solving this equation yields: This equation models the growth of Beth’s town. Use it to find the population when Beth is 16. This equation form is called a point-slope form.

If a line passes through (x1, y1) and has a slope of b, then the point-slope form of the equation is

The Point-Slope Form for Linear Equations Page 235

Silo and Jenny conducted an experiment in which Jenny walked at a constant rate. Unfortunately, Silo recorded on the data shown in the table. Elapse Time (s) Distance to the Walker (m) 3 4.6 6 2.8

Silo and Jenny conducted an experiment in which Jenny walked at a constant rate. Unfortunately, Silo recorded only the data shown in the table. Elapse Time (s) Distance to the Walker (m) 3 4.6 6 2.8

Complete steps 1-5 with your group Complete steps 1-5 with your group. Be prepared to share your thinking with the class. Elapse Time (s) Distance to the Walker (m) 3 4.6 6 2.8

Complete steps 6-8 with your group. Consider a new set of data that describe how the temperature of a pot of water changed over time as it was heated. Some of the group should create a paper graph while others use their graphing calculator to create a scatter plot. Complete steps 6-8 with your group. Time (s) Temperature (oC) 24 25 36 30 49 35 62 40 76 45 89 50

For step 9, compare your graph to others in your group For step 9, compare your graph to others in your group. Does one graph show a line that is a better fit than others. Explain. Time (s) Temperature (oC) 24 25 36 30 49 35 62 40 76 45 89 50

When do you use slope-intercept form and when do you use point-slope form? Is there a difference between the two? Explain how the two forms are similar and how they are different.

Jose’s Savings On Jose’s 16th birthday he collected all the quarters in his family’s pockets and placed them in a large jar. He decided to continue collecting quarters on his own. He counted the number of quarters in the jar periodically and recorded the data in a chart.

Jose’s Savings On Jose’s 16th birthday he collected all the quarters in his family’s pockets and placed them in a large jar. He decided to continue collecting quarters on his own. He counted the number of quarters in the jar periodically and recorded the data in a chart.

1. Make a scatter plot of the data on your calculator 1. Make a scatter plot of the data on your calculator. Describe any patterns you see in the table and/or graph. 2. Select two points that you believe represents the steepness of the line that would pass through the data. (________, ________) and (________, ________) Find the slope of the line between these two points.

Give a real world meaning to this slope. Use the slope you found to write an equation of the form y = Bx. Graph this equation with your scatter plot. Describe how the line you graphed is related to the scatter plot. What do you need to do with the line to have the line fit the data better?

Run the APPS TRANFRM on your graphing calculator Run the APPS TRANFRM on your graphing calculator. Change your equation to y=a+bx. Press WINDOW and move up to Settings. Change A to start at 0 and increase by steps of 10. Press GRAPH and notice that A=0 is printed on the screen. Use the right arrow to increase the value of A. What happens to the graph as you increase the value of A. Continue to increase or decrease the value of A until you have a line that fits the data. Write the equation for your line. Y = _____________________ What is the real world meaning for the y- intercept you located?

Use your equation to predict the number of quarters Jose will have on his 21st birthday. Explain how you predicted the number of quarters. Use your equation to predict when Jose will have collected 1000 quarters. Explain how you found your answer.