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Linear Functions

Linear Functions. Presented by: Nancy Ayers Karolee Weller. Review. Slope formula Slope-intercept equation Point-slope equation. Given two points on a line, (x 1 ,y 1 ) and (x 2 ,y 2 ), can you recall the formula for slope? m = y 2 -y 1 x 2 -x 1

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Linear Functions

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  1. Linear Functions Presented by: Nancy Ayers Karolee Weller

  2. Review • Slope formula • Slope-intercept equation • Point-slope equation Ayers/Weller

  3. Given two points on a line, (x1,y1) and (x2,y2), can you recall the formula for slope? m = y2-y1x2-x1 Then find the slope of the line that contains the points (1,2) and (3,6). m = 2-6 = -4 = 2 1-3 -2 Slope formula

  4. Point-slope equation • Do you recall this form of a linear equation? What is it used for? • y - y1 = m(x - x1) where m is the slope of the line that contains (x1,y1) • Write an equation for a line that passes through (-3,4) and has a slope of 2. • y - 4 = 2(x + 3) or simplified to y = 2x + 10 would be another equation form known as …..? Ayers/Weller

  5. Slope-intercept equation • y = mx + b where m is the slope of the line and b is the y-intercept of the line • So for the equation y = 2x + 10, 2 is the slope of the line and the line has a y-intercept of 10 Ayers/Weller

  6. Purpose When we first learned about linear equations and graphs, we started with the equations and then looked at points and graphs. Using these applications, we will see that in the real world, the points (data) actually come first and a function (equation) is created to fit the data.The function can then be used to calculate new information about the situation. Ayers/Weller

  7. OLYMPIC SPRINT--The winning times in the men’s Olympic 200-meter dash are given in the following table. • Construct a scatter plot of the data. Let t=0 represent the year 1948 and t=44 represent the year 1992. • Sketch the line that you think best approximates the points in the scatter plot. • Use two of the points to write the equation of the line. • Use the equation (or the line) to predict the winning time for this Olympic event in the year 2000.

  8. Men’s Olympic 200-meter Dash • Pick any two data points that are on or close to your line and write an equation. (32,22.03) (36,21.81) m = 21.81 - 22.03 = -.22 = -.055 36 - 32 4 y - 21.81 = -.055(x - 36) y = -.055x + 23.79 • Using this equation we can predict the winning time of this event at the 2000 Olympic games. (year 2000 = 52) y = -.055(52) + 23.79 y = 20.93

  9. INDEPENDENT PRACTICE • Anthropologists can approximate the height of a primate from the length of its humerus, the bone extending from the shoulder to the elbow. Let’s see if we can do the same with a little bit of data collection. • Form groups of five or six. • Collect the measurement of humerus bone and height of each student in your group. • Graph the data on an x/y axis system. (The humerus measurements will be x and the heights will be y.) • Sketch the line that best fits the data. • Use two points on the line to write a linear function for the line. • Use the graph or the function to predict the height of a classmate whose humerus is 12” long. How about 15” long.

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