1. Lesson 8.6 Writing Linear Equations Essential Question: How do you write linear equations?

2. Before we start… A landscape supply business charges $30 to deliver mulch. The mulch costs $23 per cubic yard. Write an equation that gives the total cost of buying and delivering mulch.

3. What is Slope-Intercept Form? Recall the graph of this equation is a line with a slope of m and a y-intercept of b.

4. How do I write an equation in slope- intercept form? Use y = mx + b Replace m with the given slope. Replace b with the given y-intercept.

10. What if you know two points on the line? If you know the point where a line crosses the y-axis and any other point on the line, you can write an equation of the line. –Calculate the slope –Use y = mx + b –Replace m with the given slope. –Replace b with the given y-intercept.

15. What about… Parallel lines? Use the same slope as the line given. Replace m with the slope. Replace b with your y- intercept. Perpendicular lines? Use the negative reciprocal slope as the line given. Replace m with the slope. Replace b with your y- intercept.

24. How do you write an equation from a table?

25. Write a rule for the function. Input, x01234 Output, y23456

26. Write a rule for the function. Input, x012345 Output, y0816243240

27. Write a rule for the function. Input, x-4-2024 Output, y13579

28. Write a rule for the function. Input, x012345 Output, y-8-7-6-5-4-3

29. What is a scatter plot? A graph used to determine whether there is a relationship between paired data. Scatter plots can show trends in the data. These trends are described by correlation.

30. What is a best-fitting line? A line drawn on a scatter plot to best estimate the relationship between two sets of data. It describes the trend of the data.

31. How do you fit a line to data? Make a scatter plot of the data. Decide whether the data can be modeled by a line. Draw a line that appears to fit the data closely. –There should be approximately as many points above the line as below it. Write an equation using two points on the line of best fit.

32. Medicine The table shows the number of female physicians in the United States for the years 1992-1999. Approximate the equation of the best-fitting line for the data. Predict the number of female physicians in 2005. Years since 1992 Female Physicians 0110 1117 2125 3140 4148 5158 6168 7177

33. Game Attendance The table shows the average attendance at a school’s varsity basketball games for various years. Write an equation that models the average attendance at varsity basketball games as a function of the number of years since 2000. YearAvg. Game Attendance 2000488 2001497 2002525 2003567 2004583 2005621 2006688

34. Grapefruit The table shows the price (in dollars) for one pound of grapefruit for the years 1997 through 2002. Write an equation that models the price of grapefruit since 1997. Years since 1997Price (dollars) 00.53 10.55 20.58 3 40.60 50.62

35. How do you write linear equations?

36. Ticket Out the Door