At the End of this Lesson…We Will Know How to: • Explain the meaning of the slope in the context of data • Explain the meaning of the y-intercept in the context of data
What Should We Know Already? • Independent Variable • Dependent Variable • Plot Points • Graph A Line • Slope • Y-Intercept
Independent Variable • A variable in an equation that may have its value freely chosen without considering values of any other variable • x value in an equation: y=mx+b x independent variable
Dependent Variable y • A variable that depends on one or more other variables • y value in an equation: y=mx+b Dependent variable
Plotting Points Points • (1,6) • (–4,2) • (0,3) • (3,0)
Graphing A Line Lines • y = –4x+5 • y = 2x+4 • y = x – 4 • y = -½x– 1
Identifying Properties of a Line Teaching Phase Example #1 slope: Y2 – Y1 X2 – X1 m = 2 y = 2x + 4 y – intercept: The value of x when the line is intersecting the y – axis b= 4
Teaching Phase: Example #2 Connor had to take a physical each year he was in his twenties and he was tested his running speed. The table shows his data from his physicals. Label the graph properly and plot each data point.
Independent Variable Connor had to take a physical each year he was in his twenties and he was tested his running speed. The table shows his data from his physicals. Label the graph properly and plot each data point. Dependent Variable 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Running Speed (MPH) 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Age
The graph below shows the amount of money babysitters made over the weekend, what could we tell? Guided Practice Example #1 Money Earned (in tens) Can we predict an estimate of the line of best fit? What is the slope telling us? What is the y-intercept telling us? If a babysitter worked for 7 hours, around how much could they make? If a babysitter earned $90, how many hours did they work? Babysitting Time (hours)
The graph below shows the amount of TV Morgan watched at night and her productivity level, what could we tell? Guided Practice Example #2 Productivity Level Hours of TV Watched Can we predict an estimate of the line of best fit? What is the slope telling us? What is the y-intercept telling us?
The table below shows the results for a long jumper and the amount of hours she had trained: Guided Practice Example #3 From the data, what can we tell? Identify the slope and y – intercept. What is the slope telling us? What is the y-intercept telling us?
WORK TIME – Independent Practice • Students need to separate into partners • Students need to identify themselves as either Partner A and Partner B • Partner A will be the reader first • Partner B will be the timer first • Partner B will tell Partner A to go and after 3 seconds Partner A will stop reading the words and count how many words they have read • This will repeat until Partner A has reached 15 seconds • Once Partner A has finished recording their data, roles will be reversed and it will be Partner B’s turn to record their data
Discussion Time • How can data be organized and represented to provide insight into the relationship between quantities? • How can I use the known information to make predictions? • How can I use known information to draw conclusions? • In context of given data, how can slope be interpreted as rate of change in a linear model? • In context of given data, how can the y – intercept be interpreted as the constant term in a linear model?