Download linear equations

LINEAR EQUATIONS
QUARTERBACK TRENDS
Linear Equations:
QUARTERBACK
Trends
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)
LINEAR EQUATIONS
QUARTERBACK TRENDS
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.
WEEK
1
COMPLETION
10
2
3
4
12
14
16
5
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:
y = mx + b
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 the
completions, and we divide it by the change in the weeks.
2
Slope =
= 2
1
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.
Slope
1+ {
1+ {
1+ {
1+ {
y-Intercept
WEEK
1
COMPLETION
10
2
3
4
12
14
16
5
18
y = mx + b
10 = (2)(1) + b
10 = 2 + b
8=b
y=2x+8
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 quarterback
have in week 10?
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)
}+2
}+2
}+2
}+2
LINEAR EQUATIONS
QUARTERBACK TRENDS
Now try the process yourself!
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 the completions, and we
divide it by the change in the weeks.
Slope =
=
+{
+{
+{
+{
WEEK
5
COMPLETION
22
6
7
8
19
16
13
9
10
Step 2: Find the y-intercept (b) by using a data point in the table.
}}}}-
y = mx + b
Step 3: Write your equation.
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?
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)