COMMON CORE STATE STANDARDS: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).6 (CCSS: 8.F.2) iv. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. (CCSS: 8.F.3) Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. (CCSS: 8.F.4) QUARTERBACK TRENDS LINEAR EQUATIONS QUARTERBACK Trends Linear Equations:
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COMMON CORE STATE STANDARDS: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).6 (CCSS: 8.F.2) iv. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. (CCSS: 8.F.3) Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. (CCSS: 8.F.4)
QUARTERBACK TRENDS
LINEAR EQUATIONS
QUARTERBACK
Trends
Linear Equations:
QUARTERBACK TRENDS
LINEAR EQUATIONS
COMMON CORE STATE STANDARDS: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).6 (CCSS: 8.F.2) iv. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. (CCSS: 8.F.3) Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. (CCSS: 8.F.4)
Today, we are going to look at quarterback trends and apply the algebra topic of linear equations in order to model statistics.
After five weeks of the season, you’ve decided to compile your favorite quarterback’s completions per game totals. The table is below.
Step 2: Find the y-intercept (b) by using a data point in the table. In the example below, we use the quarterback’s 10 completions in Week 1.
Step 3: Write your equation.
Challenge Question: If the linear equation holds true, how many completions will this quarterback have in week 10? holds true, how many completions will this quarterbackhave in week 10?
y = mx + bSlope y-Intercept
WEEK COMPLETION1
2
3
4
5
10
12
14
16
18
1+ { } + 2
1+ { } + 2
1+ { } + 2
1+ { } + 2
WEEK COMPLETION1
2
3
4
5
10
12
14
16
18
Notice that weeks are the independent variable (x) and completions are the dependent variable (y). We can take this information and model the data by creating a linear equation in slope-intercept form:
Step 1: Find the difference between the y values (Completions) and the x values (Weeks).
To find the slope (m), we take the change in thecompletions, and we divide it by the change in the weeks.
Slope = = 221
y = mx + b10 = (2)(1) + b
10 = 2 + b8 = b
y = 2 x + 8
QUARTERBACK TRENDS
LINEAR EQUATIONS
COMMON CORE STATE STANDARDS: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).6 (CCSS: 8.F.2) iv. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. (CCSS: 8.F.3) Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. (CCSS: 8.F.4)
Now try the process yourself!Step 1: Find the difference between the y values (Completions) and the x values (Weeks).
Step 2: Find the y-intercept (b) by using a data point in the table.
Step 3: Write your equation.
To find the slope (m), we take the change in the completions, and we divide it by the change in the weeks.
+ { } -
+ { } -
+ { } -
+ { } -
WEEK COMPLETION5
6
7
8
9
22
19
16
13
10Slope = =
y = mx + b
Challenge Question: If the linear equation holds true, how many completions did the quarterback have in week 2?
Challenge Question: The Coach is upset with the quarterback’s performance and states if he throws less than 5 completions in a game, he will be benched. What week is the quarterback benched?
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